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Given:
\[ \sin \theta = \frac{16}{34} \]
\[ \cos \phi = -\frac{32}{40} \]

Both angles terminate in Quadrant II. Find the exact value of \(\cos(\theta - \phi)\).

Note: Be sure to enter EXACT values. You do not need to simplify any radicals.

\[\cos(\theta - \phi) =\] _________.

Answer :

Final answer:

To find the exact value of cos(θ−ϕ) given sinθ= 16/34 and cosϕ = − 32/40, we can use the trigonometric identity cos(θ−ϕ) = cosθ cosϕ + sinθ sinϕ.

Explanation:

To find the exact value of cos(θ-φ), we can use the trigonometric identity: cos(θ-φ) = cosθ cosφ + sinθ sinφ. Since both θ and φ terminate in Quadrant II, their cosine values are negative.

Given that sinθ = 16/34 and cosφ = -32/40, we can substitute these values into the formula to find the exact value of cos(θ-φ). Therefore, cos(θ-φ) = (16/34) (-32/40) + (sqrt(1 - (16/34)^2)) (sqrt(1 - (32/40)^2)).

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