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 \\ =(-12)/(13)*(-15)/(17)+(-5)/(13)*(8)/(17) \\ =(180)/(221)-(40)/(221) \\ =(140)/(221) \end{gathered}`

Thus, the correct answer is 140/221.