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I am practicing for a test and i've come across this question which asks "What is the value of $\sin(25^\circ)$ if $\sin(155^\circ) = 0.423$?"

and I've checked on the calculator, both give same result; $0.423.$ why do they have the same value? how would you know this without using a calculator?

Michael Hardy
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Feelsbadman
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2 Answers2

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try drawing a circle sin is the height. You will see that at the angle 155 degrees it is the same height as 25 degrees.

enter image description here

Chris2018
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  • Thank you :D now i see... But shouldn't one of them give -0.42 ? instead of both giving +0.42? – Feelsbadman Jun 27 '18 at 00:18
  • they are both the same height. To get -0.42 ad 180 degrees so sin(205). – Chris2018 Jun 27 '18 at 00:21
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    I upvoted this answer. But this illustration reminds me of those images accompanying some Wikipedia articles where you can't edit them to clean up the typesetting, so you see things like $$ \begin{align} & \sin,\alpha{=}\sin,(\pi\text{-}\alpha) & \text{instead of} & \qquad \sin\alpha = \sin(\pi-\alpha) \ & \cos,(\pi\text{-}\alpha) = \text{-},\cos,\alpha & \text{instead of} & \qquad \cos(\pi-\alpha) = -\cos\alpha \end{align} $$ – Michael Hardy Jun 27 '18 at 00:36
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$$ \sin ( \pi - \alpha ) = \sin \pi \cos \alpha -\cos \pi \sin \alpha = \sin \alpha $$

Mohammad Riazi-Kermani
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