Question

Given θ is in the third quadrant and φ is in the second quadrant, sin θ=-5/13 and tanφ=-8/15 evaluate cos(θ-φ)1) 140/2212) 220/2213) -220/221

Answer 1

we know that

$\cos (\theta-\varphi)=\cos \theta\cos \varphi+\sin \theta\cos \varphi$

Now, we have to find every value in the formula using the identities.

Now, substitute the values in the formula:

$\begin{gathered} \cos (\theta-\varphi)=\cos \theta\cos \varphi+\sin \theta\sin \varphi \\ =\frac{-12}{13}\times\frac{-15}{17}+\frac{-5}{13}\times\frac{8}{17} \\ =\frac{180}{221}-\frac{40}{221} \\ =\frac{140}{221} \end{gathered}$

Thus, the correct answer is 140/221.