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sin A = 4/5 with π/2 < A < π, and cos B = -5/13 with π < B < 3π/2.

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

$\sin A = \dfrac{4}{5}$ with $\dfrac{\pi}{2} < A < \pi$ , and $\cos B = -\dfrac{5}{13}$ with $\pi < B < \dfrac{3\pi}{2}$ . Find $\sin(A - B)$ and $\cos(A + B)$ , as fractions and to three decimal places.

Need a reminder? The key ideaShow

$\cos(x \pm y) = \cos x \cos y \mp \sin x \sin y$ and $\sin(x \pm y) = \sin x \cos y \pm \cos x \sin y$ . Dividing gives $\tan(x \pm y) = \dfrac{\tan x \pm \tan y}{1 \mp \tan x \tan y}$ . The quadrant of each angle gives the sign of each ratio.

The worked solution

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sin A = 4/5 with π/2 < A < π, and cos B = -5/13 with π < B < 3π/2.

The worked solution

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