Question

If sinx + cosx = 0 and x lies in the fourth quadrant, find sin x and cos x.

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Answer 1

Answer:

sinx is -1/root 2 and cosx is 1/root2

Answer 2

Answer:

$\sin(x) = \frac{ - 1}{ \sqrt{2} } \\ \\ \cos(x) = \frac{1}{ \sqrt{2} }$

Step-by-step explanation:

If sinx + cosx = 0 and x lies in the fourth quadrant, find sin x and cos x.

$\sin(x) + \cos(x) = 0 \\ \\ \sin(x) = - \cos(x) \\ \\ \frac{sin \: x}{cos \: x} = - 1 \\ \\ tan \: x = - 1$

since x lies in fourth Quadrant,so x will be

$tan \: x = tan(2\pi - \frac{\pi}{4} ) \\ \\ x = 2\pi - \frac{\pi}{4} \\ \\ \boxed{x = \frac{7\pi}{4} =315°}$

So,

$sin \: x = \sin( \frac{7\pi}{4} ) \\ \\ sin \: x= \frac{ - 1}{ \sqrt{2} }$

same way

$\cos(x) = \cos( \frac{7\pi}{4} ) \\ \\ \cos(x)= \frac{1}{ \sqrt{2} }$

Hope it helps you.