How is $cos (pi/2+h)$ equal to $-sin(h)$? [duplicate]
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 yesterday
Xander Henderson
14.1k103554
asked yesterday
Shaikh Sakib
165
marked as duplicate by Community♦ yesterday
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 |
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 yesterday
Xander Henderson
14.1k103554
asked yesterday
Shaikh Sakib
165
marked as duplicate by Community♦ yesterday
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.
What definitions of $sin x$ and $cos x$ are you using?
– Shaun
yesterday
What is $cos(A+B)$
– lab bhattacharjee
yesterday
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.
– Shaikh Sakib
yesterday
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)?
– Xander Henderson
yesterday
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.
– Shaikh Sakib
yesterday
add a comment |
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 yesterday
Xander Henderson
14.1k103554
asked yesterday
Shaikh Sakib
165
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 yesterday
Xander Henderson
14.1k103554
asked yesterday
Shaikh Sakib
165
edited yesterday
Xander Henderson
14.1k103554
asked yesterday
Shaikh Sakib
165
edited yesterday
Xander Henderson
14.1k103554
edited yesterday
Xander Henderson
14.1k103554
edited yesterday
Xander Henderson
14.1k103554
14.1k103554
asked yesterday
Shaikh Sakib
165
asked yesterday
Shaikh Sakib
165
asked yesterday
Shaikh Sakib
165
165
marked as duplicate by Community♦ yesterday
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♦ yesterday
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.
What definitions of $sin x$ and $cos x$ are you using?
– Shaun
yesterday
What is $cos(A+B)$
– lab bhattacharjee
yesterday
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.
– Shaikh Sakib
yesterday
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)?
– Xander Henderson
yesterday
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.
– Shaikh Sakib
yesterday
add a comment |
What definitions of $sin x$ and $cos x$ are you using?
– Shaun
yesterday
What is $cos(A+B)$
– lab bhattacharjee
yesterday
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.
– Shaikh Sakib
yesterday
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)?
– Xander Henderson
yesterday
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.
– Shaikh Sakib
yesterday
What definitions of $sin x$ and $cos x$ are you using?
– Shaun
yesterday
What definitions of $sin x$ and $cos x$ are you using?
– Shaun
yesterday
What is $cos(A+B)$
– lab bhattacharjee
yesterday
What is $cos(A+B)$
– lab bhattacharjee
yesterday
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.
– Shaikh Sakib
yesterday
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.
– Shaikh Sakib
yesterday
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)?
– Xander Henderson
yesterday
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)?
– Xander Henderson
yesterday
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.
– Shaikh Sakib
yesterday
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.
– Shaikh Sakib
yesterday
add a comment |
2 Answers
2
active
oldest
votes
Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
add a comment |
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 $i^2=-1$.
answered yesterday
Shaun
8,805113680
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
add a comment |
Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
add a comment |
Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
73.3k42865
add a comment |
add a comment |
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 $i^2=-1$.
answered yesterday
Shaun
8,805113680
add a comment |
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 $i^2=-1$.
answered yesterday
Shaun
8,805113680
add a comment |
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 $i^2=-1$.
answered yesterday
Shaun
8,805113680
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 $i^2=-1$.
answered yesterday
Shaun
8,805113680
edited yesterday
answered yesterday
Shaun
8,805113680
answered yesterday
Shaun
8,805113680
answered yesterday
Shaun
8,805113680
8,805113680
add a comment |
add a comment |
What definitions of $sin x$ and $cos x$ are you using?
– Shaun
yesterday
What is $cos(A+B)$
– lab bhattacharjee
yesterday
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.
– Shaikh Sakib
yesterday
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)?
– Xander Henderson
yesterday
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.
– Shaikh Sakib
yesterday