How is $cos (pi/2+h)$ equal to $-sin(h)$? [duplicate]
$begingroup$
This question already has an answer here:
How do I prove: $cos (theta + 90^circ) equiv - sin theta $ [duplicate]
6 answers
I am not able to grasp the logic behind how $cos(frac pi2+h) = -sin(h)$.
I was able to find an explanation on Reddit but it is not clear. Can anybody elaborate in a better way?
Here is the link to the explanation - reddit link
trigonometry
edited Jan 3 at 14:40
Xander Henderson
14.8k103555
asked Jan 3 at 14:11
Shaikh SakibShaikh Sakib
195
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marked as duplicate by Community♦ Jan 3 at 14:46
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
How do I prove: $cos (theta + 90^circ) equiv - sin theta $ [duplicate]
6 answers
I am not able to grasp the logic behind how $cos(frac pi2+h) = -sin(h)$.
I was able to find an explanation on Reddit but it is not clear. Can anybody elaborate in a better way?
Here is the link to the explanation - reddit link
trigonometry
edited Jan 3 at 14:40
Xander Henderson
14.8k103555
asked Jan 3 at 14:11
Shaikh SakibShaikh Sakib
195
$endgroup$
marked as duplicate by Community♦ Jan 3 at 14:46
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
What definitions of $sin x$ and $cos x$ are you using?
$endgroup$
– Shaun
Jan 3 at 14:14
$begingroup$
What is $cos(A+B)$
$endgroup$
– lab bhattacharjee
Jan 3 at 14:14
$begingroup$
The question i am referring to is available at targetpublications.org/download/hsc-maharashtra-board/…. It is problem no xiii) and solution is given as well. Its just that the solution mentions cos(π/2+h) equal to -sinh without any explanation or citation like trig. identity. Hence needed elaboration on this.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:20
$begingroup$
The question on reddit is about computing a limit. Here you are just asking about a trigonometric identity. I am confused about what it is that you actually want to know. It would also be helpful if you could provide more context. What theorem and definitions can you work with? How are you defining the trigonometric functions (in terms of triangles? circles? power series? differential equations?)? Do you know any complex analysis (one of the answer provided below uses it)? Do you know any angle addition formulae (another answer uses that)?
$endgroup$
– Xander Henderson
Jan 3 at 14:44
$begingroup$
Yes it a limits and continuity chapter with trig. identities used in solution to simplify and arrive at a conclusion. Its just I wanted to see pattern of same kind. This solution math.stackexchange.com/questions/349495/… was what i was looking for.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:54
add a comment |
$begingroup$
This question already has an answer here:
How do I prove: $cos (theta + 90^circ) equiv - sin theta $ [duplicate]
6 answers
I am not able to grasp the logic behind how $cos(frac pi2+h) = -sin(h)$.
I was able to find an explanation on Reddit but it is not clear. Can anybody elaborate in a better way?
Here is the link to the explanation - reddit link
trigonometry
edited Jan 3 at 14:40
Xander Henderson
14.8k103555
asked Jan 3 at 14:11
Shaikh SakibShaikh Sakib
195
$endgroup$
This question already has an answer here:
How do I prove: $cos (theta + 90^circ) equiv - sin theta $ [duplicate]
6 answers
I am not able to grasp the logic behind how $cos(frac pi2+h) = -sin(h)$.
I was able to find an explanation on Reddit but it is not clear. Can anybody elaborate in a better way?
Here is the link to the explanation - reddit link
This question already has an answer here:
How do I prove: $cos (theta + 90^circ) equiv - sin theta $ [duplicate]
6 answers
trigonometry
trigonometry
edited Jan 3 at 14:40
Xander Henderson
14.8k103555
asked Jan 3 at 14:11
Shaikh SakibShaikh Sakib
195
edited Jan 3 at 14:40
Xander Henderson
14.8k103555
asked Jan 3 at 14:11
Shaikh SakibShaikh Sakib
195
edited Jan 3 at 14:40
Xander Henderson
14.8k103555
edited Jan 3 at 14:40
Xander Henderson
14.8k103555
edited Jan 3 at 14:40
Xander Henderson
14.8k103555
14.8k103555
asked Jan 3 at 14:11
Shaikh SakibShaikh Sakib
195
asked Jan 3 at 14:11
Shaikh SakibShaikh Sakib
195
asked Jan 3 at 14:11
Shaikh SakibShaikh Sakib
195
195
marked as duplicate by Community♦ Jan 3 at 14:46
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Community♦ Jan 3 at 14:46
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
What definitions of $sin x$ and $cos x$ are you using?
$endgroup$
– Shaun
Jan 3 at 14:14
$begingroup$
What is $cos(A+B)$
$endgroup$
– lab bhattacharjee
Jan 3 at 14:14
$begingroup$
The question i am referring to is available at targetpublications.org/download/hsc-maharashtra-board/…. It is problem no xiii) and solution is given as well. Its just that the solution mentions cos(π/2+h) equal to -sinh without any explanation or citation like trig. identity. Hence needed elaboration on this.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:20
$begingroup$
The question on reddit is about computing a limit. Here you are just asking about a trigonometric identity. I am confused about what it is that you actually want to know. It would also be helpful if you could provide more context. What theorem and definitions can you work with? How are you defining the trigonometric functions (in terms of triangles? circles? power series? differential equations?)? Do you know any complex analysis (one of the answer provided below uses it)? Do you know any angle addition formulae (another answer uses that)?
$endgroup$
– Xander Henderson
Jan 3 at 14:44
$begingroup$
Yes it a limits and continuity chapter with trig. identities used in solution to simplify and arrive at a conclusion. Its just I wanted to see pattern of same kind. This solution math.stackexchange.com/questions/349495/… was what i was looking for.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:54
add a comment |
$begingroup$
What definitions of $sin x$ and $cos x$ are you using?
$endgroup$
– Shaun
Jan 3 at 14:14
$begingroup$
What is $cos(A+B)$
$endgroup$
– lab bhattacharjee
Jan 3 at 14:14
$begingroup$
The question i am referring to is available at targetpublications.org/download/hsc-maharashtra-board/…. It is problem no xiii) and solution is given as well. Its just that the solution mentions cos(π/2+h) equal to -sinh without any explanation or citation like trig. identity. Hence needed elaboration on this.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:20
$begingroup$
The question on reddit is about computing a limit. Here you are just asking about a trigonometric identity. I am confused about what it is that you actually want to know. It would also be helpful if you could provide more context. What theorem and definitions can you work with? How are you defining the trigonometric functions (in terms of triangles? circles? power series? differential equations?)? Do you know any complex analysis (one of the answer provided below uses it)? Do you know any angle addition formulae (another answer uses that)?
$endgroup$
– Xander Henderson
Jan 3 at 14:44
$begingroup$
Yes it a limits and continuity chapter with trig. identities used in solution to simplify and arrive at a conclusion. Its just I wanted to see pattern of same kind. This solution math.stackexchange.com/questions/349495/… was what i was looking for.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:54
$begingroup$
What definitions of $sin x$ and $cos x$ are you using?
$endgroup$
– Shaun
Jan 3 at 14:14
$begingroup$
What definitions of $sin x$ and $cos x$ are you using?
$endgroup$
– Shaun
Jan 3 at 14:14
$begingroup$
What is $cos(A+B)$
$endgroup$
– lab bhattacharjee
Jan 3 at 14:14
$begingroup$
What is $cos(A+B)$
$endgroup$
– lab bhattacharjee
Jan 3 at 14:14
$begingroup$
The question i am referring to is available at targetpublications.org/download/hsc-maharashtra-board/…. It is problem no xiii) and solution is given as well. Its just that the solution mentions cos(π/2+h) equal to -sinh without any explanation or citation like trig. identity. Hence needed elaboration on this.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:20
$begingroup$
The question i am referring to is available at targetpublications.org/download/hsc-maharashtra-board/…. It is problem no xiii) and solution is given as well. Its just that the solution mentions cos(π/2+h) equal to -sinh without any explanation or citation like trig. identity. Hence needed elaboration on this.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:20
$begingroup$
The question on reddit is about computing a limit. Here you are just asking about a trigonometric identity. I am confused about what it is that you actually want to know. It would also be helpful if you could provide more context. What theorem and definitions can you work with? How are you defining the trigonometric functions (in terms of triangles? circles? power series? differential equations?)? Do you know any complex analysis (one of the answer provided below uses it)? Do you know any angle addition formulae (another answer uses that)?
$endgroup$
– Xander Henderson
Jan 3 at 14:44
$begingroup$
The question on reddit is about computing a limit. Here you are just asking about a trigonometric identity. I am confused about what it is that you actually want to know. It would also be helpful if you could provide more context. What theorem and definitions can you work with? How are you defining the trigonometric functions (in terms of triangles? circles? power series? differential equations?)? Do you know any complex analysis (one of the answer provided below uses it)? Do you know any angle addition formulae (another answer uses that)?
$endgroup$
– Xander Henderson
Jan 3 at 14:44
$begingroup$
Yes it a limits and continuity chapter with trig. identities used in solution to simplify and arrive at a conclusion. Its just I wanted to see pattern of same kind. This solution math.stackexchange.com/questions/349495/… was what i was looking for.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:54
$begingroup$
Yes it a limits and continuity chapter with trig. identities used in solution to simplify and arrive at a conclusion. Its just I wanted to see pattern of same kind. This solution math.stackexchange.com/questions/349495/… was what i was looking for.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:54
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$
answered Jan 3 at 14:15
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
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add a comment |
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Hint: One way to define $cos x$ is $$frac{e^{ix}+e^{-ix}}{2}$$ and, similarly, one can write $sin x$ as $$frac{e^{ix}-e^{-ix}}{2i},$$ where $i$ is defined such that $i^2=-1$. Use $e^{ipi}=-1$.
answered Jan 3 at 14:29
ShaunShaun
9,366113684
$endgroup$
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$
answered Jan 3 at 14:15
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
$endgroup$
add a comment |
$begingroup$
Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$
answered Jan 3 at 14:15
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
$endgroup$
add a comment |
$begingroup$
Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$
answered Jan 3 at 14:15
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
$endgroup$
Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$
answered Jan 3 at 14:15
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
answered Jan 3 at 14:15
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
answered Jan 3 at 14:15
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
answered Jan 3 at 14:15
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
76.8k42866
76.8k42866
add a comment |
add a comment |
$begingroup$
Hint: One way to define $cos x$ is $$frac{e^{ix}+e^{-ix}}{2}$$ and, similarly, one can write $sin x$ as $$frac{e^{ix}-e^{-ix}}{2i},$$ where $i$ is defined such that $i^2=-1$. Use $e^{ipi}=-1$.
answered Jan 3 at 14:29
ShaunShaun
9,366113684
$endgroup$
add a comment |
$begingroup$
Hint: One way to define $cos x$ is $$frac{e^{ix}+e^{-ix}}{2}$$ and, similarly, one can write $sin x$ as $$frac{e^{ix}-e^{-ix}}{2i},$$ where $i$ is defined such that $i^2=-1$. Use $e^{ipi}=-1$.
answered Jan 3 at 14:29
ShaunShaun
9,366113684
$endgroup$
add a comment |
$begingroup$
Hint: One way to define $cos x$ is $$frac{e^{ix}+e^{-ix}}{2}$$ and, similarly, one can write $sin x$ as $$frac{e^{ix}-e^{-ix}}{2i},$$ where $i$ is defined such that $i^2=-1$. Use $e^{ipi}=-1$.
answered Jan 3 at 14:29
ShaunShaun
9,366113684
$endgroup$
Hint: One way to define $cos x$ is $$frac{e^{ix}+e^{-ix}}{2}$$ and, similarly, one can write $sin x$ as $$frac{e^{ix}-e^{-ix}}{2i},$$ where $i$ is defined such that $i^2=-1$. Use $e^{ipi}=-1$.
answered Jan 3 at 14:29
ShaunShaun
9,366113684
edited Jan 12 at 9:59
answered Jan 3 at 14:29
ShaunShaun
9,366113684
answered Jan 3 at 14:29
ShaunShaun
9,366113684
answered Jan 3 at 14:29
ShaunShaun
9,366113684
9,366113684
add a comment |
add a comment |
$begingroup$
What definitions of $sin x$ and $cos x$ are you using?
$endgroup$
– Shaun
Jan 3 at 14:14
$begingroup$
What is $cos(A+B)$
$endgroup$
– lab bhattacharjee
Jan 3 at 14:14
$begingroup$
The question i am referring to is available at targetpublications.org/download/hsc-maharashtra-board/…. It is problem no xiii) and solution is given as well. Its just that the solution mentions cos(π/2+h) equal to -sinh without any explanation or citation like trig. identity. Hence needed elaboration on this.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:20
$begingroup$
The question on reddit is about computing a limit. Here you are just asking about a trigonometric identity. I am confused about what it is that you actually want to know. It would also be helpful if you could provide more context. What theorem and definitions can you work with? How are you defining the trigonometric functions (in terms of triangles? circles? power series? differential equations?)? Do you know any complex analysis (one of the answer provided below uses it)? Do you know any angle addition formulae (another answer uses that)?
$endgroup$
– Xander Henderson
Jan 3 at 14:44
$begingroup$
Yes it a limits and continuity chapter with trig. identities used in solution to simplify and arrive at a conclusion. Its just I wanted to see pattern of same kind. This solution math.stackexchange.com/questions/349495/… was what i was looking for.
$endgroup$
– Shaikh Sakib
Jan 3 at 14:54