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=(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 ((\pi)/(2)-\theta) \\ \sin (35.68)=\cos ((\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=(7)/(12) \\ 2\theta=\sin ^(-1)((7)/(12)) \\ 2\theta=17.84 \end{gathered}`

Is the answer clear?