Question
Assuming that $\sin \theta=0.6249$ and $\cos \phi=0.1102$ and that both $\theta$ and $\phi$ are first-quadrant angles, evaluate each of the following.$$\tan (\theta+\phi)$$
Step 1
We know that $\sin^2 \theta + \cos^2 \theta = 1$ and $\sin^2 \phi + \cos^2 \phi = 1$. So, we can find $\cos \theta = \sqrt{1 - \sin^2 \theta} = \sqrt{1 - 0.6249^2} = 0.7807$ and $\sin \phi = \sqrt{1 - \cos^2 \phi} = \sqrt{1 - 0.1102^2} = 0.9939$. Show more…
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