Simplify tan$theta$ cos$theta$
$begingroup$
How do I simplify tan$theta$ cos$theta$ ?
Why is this so hard to do? What pieces of information should I know before doing these?
Can someone just tell me were am I going wrong? I have 5 days to master this before my SAT Practice.
I would brush up on 'basics' but i don't even know how this related to anything ive learnt in trig before...I literally google every identity, am i supposed to remember or somehow derive them??
algebra-precalculus trigonometry
$endgroup$
|
show 3 more comments
$begingroup$
How do I simplify tan$theta$ cos$theta$ ?
Why is this so hard to do? What pieces of information should I know before doing these?
Can someone just tell me were am I going wrong? I have 5 days to master this before my SAT Practice.
I would brush up on 'basics' but i don't even know how this related to anything ive learnt in trig before...I literally google every identity, am i supposed to remember or somehow derive them??
algebra-precalculus trigonometry
$endgroup$
5
$begingroup$
Do you remember the definition of tan?
$endgroup$
– Mathmo123
Jul 22 '14 at 10:27
1
$begingroup$
Do you know how tan relates to sin and cos? (4 days, 23h, 58min)
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:28
$begingroup$
sosmath.com/trig/Trig5/trig5/trig5.html
$endgroup$
– Scientifica
Jul 22 '14 at 10:28
$begingroup$
To use the 5 days brushing up the basics will be worth more than collecting and memorising possible answers
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:34
$begingroup$
I saw your earlier posts. You are going wrong, by not concentrating on the basic definition of sine, cos and tan. If I was you, I would take a pen and paper and start by drawing triangle and learn the ratios of sin,cos and tan. It would not be called maths, if it was not tricky! :)
$endgroup$
– MonK
Jul 22 '14 at 10:35
|
show 3 more comments
$begingroup$
How do I simplify tan$theta$ cos$theta$ ?
Why is this so hard to do? What pieces of information should I know before doing these?
Can someone just tell me were am I going wrong? I have 5 days to master this before my SAT Practice.
I would brush up on 'basics' but i don't even know how this related to anything ive learnt in trig before...I literally google every identity, am i supposed to remember or somehow derive them??
algebra-precalculus trigonometry
$endgroup$
How do I simplify tan$theta$ cos$theta$ ?
Why is this so hard to do? What pieces of information should I know before doing these?
Can someone just tell me were am I going wrong? I have 5 days to master this before my SAT Practice.
I would brush up on 'basics' but i don't even know how this related to anything ive learnt in trig before...I literally google every identity, am i supposed to remember or somehow derive them??
algebra-precalculus trigonometry
algebra-precalculus trigonometry
edited Jul 22 '14 at 10:59
Brad
4,27021448
4,27021448
asked Jul 22 '14 at 10:26
sashasasha
214
214
5
$begingroup$
Do you remember the definition of tan?
$endgroup$
– Mathmo123
Jul 22 '14 at 10:27
1
$begingroup$
Do you know how tan relates to sin and cos? (4 days, 23h, 58min)
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:28
$begingroup$
sosmath.com/trig/Trig5/trig5/trig5.html
$endgroup$
– Scientifica
Jul 22 '14 at 10:28
$begingroup$
To use the 5 days brushing up the basics will be worth more than collecting and memorising possible answers
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:34
$begingroup$
I saw your earlier posts. You are going wrong, by not concentrating on the basic definition of sine, cos and tan. If I was you, I would take a pen and paper and start by drawing triangle and learn the ratios of sin,cos and tan. It would not be called maths, if it was not tricky! :)
$endgroup$
– MonK
Jul 22 '14 at 10:35
|
show 3 more comments
5
$begingroup$
Do you remember the definition of tan?
$endgroup$
– Mathmo123
Jul 22 '14 at 10:27
1
$begingroup$
Do you know how tan relates to sin and cos? (4 days, 23h, 58min)
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:28
$begingroup$
sosmath.com/trig/Trig5/trig5/trig5.html
$endgroup$
– Scientifica
Jul 22 '14 at 10:28
$begingroup$
To use the 5 days brushing up the basics will be worth more than collecting and memorising possible answers
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:34
$begingroup$
I saw your earlier posts. You are going wrong, by not concentrating on the basic definition of sine, cos and tan. If I was you, I would take a pen and paper and start by drawing triangle and learn the ratios of sin,cos and tan. It would not be called maths, if it was not tricky! :)
$endgroup$
– MonK
Jul 22 '14 at 10:35
5
5
$begingroup$
Do you remember the definition of tan?
$endgroup$
– Mathmo123
Jul 22 '14 at 10:27
$begingroup$
Do you remember the definition of tan?
$endgroup$
– Mathmo123
Jul 22 '14 at 10:27
1
1
$begingroup$
Do you know how tan relates to sin and cos? (4 days, 23h, 58min)
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:28
$begingroup$
Do you know how tan relates to sin and cos? (4 days, 23h, 58min)
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:28
$begingroup$
sosmath.com/trig/Trig5/trig5/trig5.html
$endgroup$
– Scientifica
Jul 22 '14 at 10:28
$begingroup$
sosmath.com/trig/Trig5/trig5/trig5.html
$endgroup$
– Scientifica
Jul 22 '14 at 10:28
$begingroup$
To use the 5 days brushing up the basics will be worth more than collecting and memorising possible answers
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:34
$begingroup$
To use the 5 days brushing up the basics will be worth more than collecting and memorising possible answers
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:34
$begingroup$
I saw your earlier posts. You are going wrong, by not concentrating on the basic definition of sine, cos and tan. If I was you, I would take a pen and paper and start by drawing triangle and learn the ratios of sin,cos and tan. It would not be called maths, if it was not tricky! :)
$endgroup$
– MonK
Jul 22 '14 at 10:35
$begingroup$
I saw your earlier posts. You are going wrong, by not concentrating on the basic definition of sine, cos and tan. If I was you, I would take a pen and paper and start by drawing triangle and learn the ratios of sin,cos and tan. It would not be called maths, if it was not tricky! :)
$endgroup$
– MonK
Jul 22 '14 at 10:35
|
show 3 more comments
4 Answers
4
active
oldest
votes
$begingroup$
Hint: What is the definition of the $tan$ function?
$endgroup$
$begingroup$
Tan = Opp / Adj..
$endgroup$
– sasha
Jul 22 '14 at 10:38
1
$begingroup$
@sasha That is a rough definition only true for angles from $0$ to $fracpi2$. For other corners, the $tan$ is defined via the $cos$ and $sin$ function. If you are practising for SATs, I advise you to look that definition up.
$endgroup$
– 5xum
Jul 22 '14 at 10:40
$begingroup$
@sasha $tantheta = opp/adj = displaystylefrac{opp}{adj}cdotfrac{frac{1}{hyp}}{frac{1}{hyp}} = frac{frac{opp}{hyp}}{frac{opp}{hyp}}=frac{sintheta}{costheta}$
$endgroup$
– John Joy
Jul 22 '14 at 13:30
add a comment |
$begingroup$
Notice first that the $tan$ function is defined on $D:=Bbb Rsetminus{fracpi2+kpi,; kinBbb Z}$ and that $tantheta=frac{sintheta}{costheta}$ so
$$tanthetacostheta=sintheta,quadforallthetain D$$
and be careful the trap is to give a wrong domain.
$endgroup$
$begingroup$
I am used to write-
rather than $$ for excluding. Anyway +1
$endgroup$
– mrs
Jul 22 '14 at 12:21
add a comment |
$begingroup$
Elementary school proof for $theta in ]0, pi/2[$:
Consider a right triangle with angles $pi/2, theta, pi/2-theta$ and edges lengths $a,b,c>0$ as in the figure below
Then
$$tan(theta)= frac{a}{c}, quad cos(theta) = frac{c}{b}, quad sin(theta) = frac{a}{b},$$
thus
$$tan(theta) cos(theta) = frac{a}{c}cdot frac{c}{b} = frac{a}{b} = sin(theta).$$
$endgroup$
add a comment |
$begingroup$
There are two ways to do this.
Here is one way:
Saying that
$tan(x)=o/a $ and $ cos(x)=a/h$, we get $oa/ha = o/h=sin x$ so the answer is $sin x$!
$endgroup$
add a comment |
Your Answer
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint: What is the definition of the $tan$ function?
$endgroup$
$begingroup$
Tan = Opp / Adj..
$endgroup$
– sasha
Jul 22 '14 at 10:38
1
$begingroup$
@sasha That is a rough definition only true for angles from $0$ to $fracpi2$. For other corners, the $tan$ is defined via the $cos$ and $sin$ function. If you are practising for SATs, I advise you to look that definition up.
$endgroup$
– 5xum
Jul 22 '14 at 10:40
$begingroup$
@sasha $tantheta = opp/adj = displaystylefrac{opp}{adj}cdotfrac{frac{1}{hyp}}{frac{1}{hyp}} = frac{frac{opp}{hyp}}{frac{opp}{hyp}}=frac{sintheta}{costheta}$
$endgroup$
– John Joy
Jul 22 '14 at 13:30
add a comment |
$begingroup$
Hint: What is the definition of the $tan$ function?
$endgroup$
$begingroup$
Tan = Opp / Adj..
$endgroup$
– sasha
Jul 22 '14 at 10:38
1
$begingroup$
@sasha That is a rough definition only true for angles from $0$ to $fracpi2$. For other corners, the $tan$ is defined via the $cos$ and $sin$ function. If you are practising for SATs, I advise you to look that definition up.
$endgroup$
– 5xum
Jul 22 '14 at 10:40
$begingroup$
@sasha $tantheta = opp/adj = displaystylefrac{opp}{adj}cdotfrac{frac{1}{hyp}}{frac{1}{hyp}} = frac{frac{opp}{hyp}}{frac{opp}{hyp}}=frac{sintheta}{costheta}$
$endgroup$
– John Joy
Jul 22 '14 at 13:30
add a comment |
$begingroup$
Hint: What is the definition of the $tan$ function?
$endgroup$
Hint: What is the definition of the $tan$ function?
answered Jul 22 '14 at 10:28
5xum5xum
90.6k394161
90.6k394161
$begingroup$
Tan = Opp / Adj..
$endgroup$
– sasha
Jul 22 '14 at 10:38
1
$begingroup$
@sasha That is a rough definition only true for angles from $0$ to $fracpi2$. For other corners, the $tan$ is defined via the $cos$ and $sin$ function. If you are practising for SATs, I advise you to look that definition up.
$endgroup$
– 5xum
Jul 22 '14 at 10:40
$begingroup$
@sasha $tantheta = opp/adj = displaystylefrac{opp}{adj}cdotfrac{frac{1}{hyp}}{frac{1}{hyp}} = frac{frac{opp}{hyp}}{frac{opp}{hyp}}=frac{sintheta}{costheta}$
$endgroup$
– John Joy
Jul 22 '14 at 13:30
add a comment |
$begingroup$
Tan = Opp / Adj..
$endgroup$
– sasha
Jul 22 '14 at 10:38
1
$begingroup$
@sasha That is a rough definition only true for angles from $0$ to $fracpi2$. For other corners, the $tan$ is defined via the $cos$ and $sin$ function. If you are practising for SATs, I advise you to look that definition up.
$endgroup$
– 5xum
Jul 22 '14 at 10:40
$begingroup$
@sasha $tantheta = opp/adj = displaystylefrac{opp}{adj}cdotfrac{frac{1}{hyp}}{frac{1}{hyp}} = frac{frac{opp}{hyp}}{frac{opp}{hyp}}=frac{sintheta}{costheta}$
$endgroup$
– John Joy
Jul 22 '14 at 13:30
$begingroup$
Tan = Opp / Adj..
$endgroup$
– sasha
Jul 22 '14 at 10:38
$begingroup$
Tan = Opp / Adj..
$endgroup$
– sasha
Jul 22 '14 at 10:38
1
1
$begingroup$
@sasha That is a rough definition only true for angles from $0$ to $fracpi2$. For other corners, the $tan$ is defined via the $cos$ and $sin$ function. If you are practising for SATs, I advise you to look that definition up.
$endgroup$
– 5xum
Jul 22 '14 at 10:40
$begingroup$
@sasha That is a rough definition only true for angles from $0$ to $fracpi2$. For other corners, the $tan$ is defined via the $cos$ and $sin$ function. If you are practising for SATs, I advise you to look that definition up.
$endgroup$
– 5xum
Jul 22 '14 at 10:40
$begingroup$
@sasha $tantheta = opp/adj = displaystylefrac{opp}{adj}cdotfrac{frac{1}{hyp}}{frac{1}{hyp}} = frac{frac{opp}{hyp}}{frac{opp}{hyp}}=frac{sintheta}{costheta}$
$endgroup$
– John Joy
Jul 22 '14 at 13:30
$begingroup$
@sasha $tantheta = opp/adj = displaystylefrac{opp}{adj}cdotfrac{frac{1}{hyp}}{frac{1}{hyp}} = frac{frac{opp}{hyp}}{frac{opp}{hyp}}=frac{sintheta}{costheta}$
$endgroup$
– John Joy
Jul 22 '14 at 13:30
add a comment |
$begingroup$
Notice first that the $tan$ function is defined on $D:=Bbb Rsetminus{fracpi2+kpi,; kinBbb Z}$ and that $tantheta=frac{sintheta}{costheta}$ so
$$tanthetacostheta=sintheta,quadforallthetain D$$
and be careful the trap is to give a wrong domain.
$endgroup$
$begingroup$
I am used to write-
rather than $$ for excluding. Anyway +1
$endgroup$
– mrs
Jul 22 '14 at 12:21
add a comment |
$begingroup$
Notice first that the $tan$ function is defined on $D:=Bbb Rsetminus{fracpi2+kpi,; kinBbb Z}$ and that $tantheta=frac{sintheta}{costheta}$ so
$$tanthetacostheta=sintheta,quadforallthetain D$$
and be careful the trap is to give a wrong domain.
$endgroup$
$begingroup$
I am used to write-
rather than $$ for excluding. Anyway +1
$endgroup$
– mrs
Jul 22 '14 at 12:21
add a comment |
$begingroup$
Notice first that the $tan$ function is defined on $D:=Bbb Rsetminus{fracpi2+kpi,; kinBbb Z}$ and that $tantheta=frac{sintheta}{costheta}$ so
$$tanthetacostheta=sintheta,quadforallthetain D$$
and be careful the trap is to give a wrong domain.
$endgroup$
Notice first that the $tan$ function is defined on $D:=Bbb Rsetminus{fracpi2+kpi,; kinBbb Z}$ and that $tantheta=frac{sintheta}{costheta}$ so
$$tanthetacostheta=sintheta,quadforallthetain D$$
and be careful the trap is to give a wrong domain.
answered Jul 22 '14 at 10:36
user63181
$begingroup$
I am used to write-
rather than $$ for excluding. Anyway +1
$endgroup$
– mrs
Jul 22 '14 at 12:21
add a comment |
$begingroup$
I am used to write-
rather than $$ for excluding. Anyway +1
$endgroup$
– mrs
Jul 22 '14 at 12:21
$begingroup$
I am used to write
-
rather than $$ for excluding. Anyway +1$endgroup$
– mrs
Jul 22 '14 at 12:21
$begingroup$
I am used to write
-
rather than $$ for excluding. Anyway +1$endgroup$
– mrs
Jul 22 '14 at 12:21
add a comment |
$begingroup$
Elementary school proof for $theta in ]0, pi/2[$:
Consider a right triangle with angles $pi/2, theta, pi/2-theta$ and edges lengths $a,b,c>0$ as in the figure below
Then
$$tan(theta)= frac{a}{c}, quad cos(theta) = frac{c}{b}, quad sin(theta) = frac{a}{b},$$
thus
$$tan(theta) cos(theta) = frac{a}{c}cdot frac{c}{b} = frac{a}{b} = sin(theta).$$
$endgroup$
add a comment |
$begingroup$
Elementary school proof for $theta in ]0, pi/2[$:
Consider a right triangle with angles $pi/2, theta, pi/2-theta$ and edges lengths $a,b,c>0$ as in the figure below
Then
$$tan(theta)= frac{a}{c}, quad cos(theta) = frac{c}{b}, quad sin(theta) = frac{a}{b},$$
thus
$$tan(theta) cos(theta) = frac{a}{c}cdot frac{c}{b} = frac{a}{b} = sin(theta).$$
$endgroup$
add a comment |
$begingroup$
Elementary school proof for $theta in ]0, pi/2[$:
Consider a right triangle with angles $pi/2, theta, pi/2-theta$ and edges lengths $a,b,c>0$ as in the figure below
Then
$$tan(theta)= frac{a}{c}, quad cos(theta) = frac{c}{b}, quad sin(theta) = frac{a}{b},$$
thus
$$tan(theta) cos(theta) = frac{a}{c}cdot frac{c}{b} = frac{a}{b} = sin(theta).$$
$endgroup$
Elementary school proof for $theta in ]0, pi/2[$:
Consider a right triangle with angles $pi/2, theta, pi/2-theta$ and edges lengths $a,b,c>0$ as in the figure below
Then
$$tan(theta)= frac{a}{c}, quad cos(theta) = frac{c}{b}, quad sin(theta) = frac{a}{b},$$
thus
$$tan(theta) cos(theta) = frac{a}{c}cdot frac{c}{b} = frac{a}{b} = sin(theta).$$
answered Jul 22 '14 at 12:02
SurbSurb
37.7k94375
37.7k94375
add a comment |
add a comment |
$begingroup$
There are two ways to do this.
Here is one way:
Saying that
$tan(x)=o/a $ and $ cos(x)=a/h$, we get $oa/ha = o/h=sin x$ so the answer is $sin x$!
$endgroup$
add a comment |
$begingroup$
There are two ways to do this.
Here is one way:
Saying that
$tan(x)=o/a $ and $ cos(x)=a/h$, we get $oa/ha = o/h=sin x$ so the answer is $sin x$!
$endgroup$
add a comment |
$begingroup$
There are two ways to do this.
Here is one way:
Saying that
$tan(x)=o/a $ and $ cos(x)=a/h$, we get $oa/ha = o/h=sin x$ so the answer is $sin x$!
$endgroup$
There are two ways to do this.
Here is one way:
Saying that
$tan(x)=o/a $ and $ cos(x)=a/h$, we get $oa/ha = o/h=sin x$ so the answer is $sin x$!
edited Dec 12 '18 at 1:15
amWhy
1
1
answered Dec 12 '18 at 1:09
A.usernemaA.usernema
113
113
add a comment |
add a comment |
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5
$begingroup$
Do you remember the definition of tan?
$endgroup$
– Mathmo123
Jul 22 '14 at 10:27
1
$begingroup$
Do you know how tan relates to sin and cos? (4 days, 23h, 58min)
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:28
$begingroup$
sosmath.com/trig/Trig5/trig5/trig5.html
$endgroup$
– Scientifica
Jul 22 '14 at 10:28
$begingroup$
To use the 5 days brushing up the basics will be worth more than collecting and memorising possible answers
$endgroup$
– Lord_Gestalter
Jul 22 '14 at 10:34
$begingroup$
I saw your earlier posts. You are going wrong, by not concentrating on the basic definition of sine, cos and tan. If I was you, I would take a pen and paper and start by drawing triangle and learn the ratios of sin,cos and tan. It would not be called maths, if it was not tricky! :)
$endgroup$
– MonK
Jul 22 '14 at 10:35