How is $cos (pi/2+h)$ equal to $-sin(h)$? [duplicate]












-2















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







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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
















-2















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







share|cite|improve this 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














-2












-2








-2








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







share|cite|improve this question
















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited yesterday









Xander Henderson

14.1k103554




14.1k103554










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


















  • 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










2 Answers
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Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$






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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 $i^2=-1$.






    share|cite|improve this answer






























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      0














      Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$






      share|cite|improve this answer


























        0














        Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$






        share|cite|improve this answer
























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          0








          0






          Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$






          share|cite|improve this answer












          Use that $$cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered yesterday









          Dr. Sonnhard Graubner

          73.3k42865




          73.3k42865























              0














              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 $i^2=-1$.






              share|cite|improve this answer




























                0














                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 $i^2=-1$.






                share|cite|improve this answer


























                  0












                  0








                  0






                  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 $i^2=-1$.






                  share|cite|improve this answer














                  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 $i^2=-1$.







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited yesterday

























                  answered yesterday









                  Shaun

                  8,805113680




                  8,805113680















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