Question

Use the side lengths of the triangle to numerically verify the following trig identities. Also, draw a triangle, in relation the one one above, with an angle measure of 2 theta.

Answer 1

Given,

As we know,

$\begin{gathered} \sin \theta=\frac{7}{12} \\ \theta=35.68 \end{gathered}$

Taking the first identity,

$\begin{gathered} \sin ^2\theta+\cos ^2\theta=1 \\ \sin ^2(35.68)+\cos ^2(35.68)=0.3401+0.6598 \\ =1 \end{gathered}$

Now, taking another quantity.

$\begin{gathered} \sin \theta=\cos (\frac{\pi}{2}-\theta) \\ \sin (35.68)=\cos (\frac{\pi}{2}-35.68) \\ \sin (35.68)=\cos (144.32) \\ 0.5832=0.5832 \end{gathered}$

From the same method, we can solve different quantities.

Drawing another triangle with the angle measure of

The angle will be,

$\begin{gathered} \sin 2\theta=\frac{7}{12} \\ 2\theta=\sin ^{-1}(\frac{7}{12}) \\ 2\theta=17.84 \end{gathered}$

Is the answer clear?