Question

Trigonometry question

Answer 1

\[\cos \alpha = -\frac{4}5= 2 \cos^2 \alpha/2 - 1\]\[\pi/2 \le \alpha/2 \le 3\pi/4 \Rightarrow \cos \alpha/2 < 0\]

Answer 2

sin(37)=3/5
sin(180+37)=-3/5

Answer 3

\(\large \color{black}{\begin{align}
&\cos \dfrac{\alpha}{2}=\dfrac{1}{\sqrt{10}} \text{}\hspace{.33em}\\~\\
\end{align}}\)

Answer 4

I told you that \(\cos\alpha/2\) is negative because \( \pi/2\le \alpha/2\le 3\pi/4\). On the unit circle, those angles have a negative x-coordinate.

Answer 5

\(\large \color{black}{\begin{align}
&\cos \dfrac{\alpha}{2}=-\dfrac{1}{\sqrt{10}} \text{}\hspace{.33em}\\~\\
\end{align}}\)