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An angle x lies between π/2 and π, and tan x = -3/4. Find sin x and cos x.

Contributed by StemPy Lab

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

An angle $x$ lies between $\dfrac{\pi}{2}$ and $\pi$ , and $\tan x = -\dfrac{3}{4}$ . Find $\sin x$ and $\cos x$ .

Need a reminder? The key ideaShow

On the unit circle, the point reached by turning through $x$ from $A(1, 0)$ is $P = (\cos x, \sin x)$ . So $\sin^2 x + \cos^2 x = 1$ , and $1 + \tan^2 x = \sec^2 x$ . The sign of $\cos x$ is the sign of the x-coordinate of $P$ , and the sign of $\sin x$ is the sign of its y-coordinate.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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