Sine and Cosine of Obtuse Angles

If  $\theta$  is an obtuse angle, which of the following formula about  $\sin\theta$  is correct?

•  $\sin\theta=-\sin\theta$  

•  $\sin\theta=-\sin\left(180\degree-\theta\right)$  

•  $\sin\theta=\sin\left(180\degree-\theta\right)$  

•  $\sin\theta=\cos\theta$  

If  $\theta$  is an obtuse angle, which of the following formula about  $\cos\theta$  is correct?

•  $\cos\theta=-\sin\theta$  

•  $\cos\theta=-\cos\left(180\degree-\theta\right)$  

•  $\cos\theta=\cos\left(180\degree-\theta\right)$  

•  $\cos\theta=-\cos\theta$  

The formula $\sin\theta=\sin\left(180\degree-\theta\right)$ tells us that there is/are ____ answer(s) to the equation  $\sin\theta=0.52$  . 

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The formula $\cos\theta=-\cos\left(180\degree-\theta\right)$ tells us that there is/are ____ answer(s) to the equation  $\cos\theta=0.52$  . 

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From this screenshot of Mr Lee's notes, we can make the following conclusions.

• If $\angle a$ is acute, then $\cos\angle a$ is positive.

• If $\angle a$ is acute, then $\angle b$ is obtuse.

• If $\angle b$ is obtuse, then $\cos\angle b$ is negative.

• Mr Lee is lazy and did not do his work. :/

Select all answer(s) to the equation  $\sin\theta=0.52$  

•  $\theta=31.3\degree$  

•  $\theta=148.7\degree$  

• This equation cannot be solved.