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dimulka [17.4K]
3 years ago
11

1. Find sin? if cos?=1/2 and ? terminates in Quadrant IV. 2. Find cos? if sin?=(?2)/2 and ? terminates in Quadrant I. 3. Find ta

n? if cos?=-1/2 and ? terminates in Quadrant II. 4. Find tan? if sin?=-1 and 0??<2? radians.
Mathematics
1 answer:
mina [271]3 years ago
4 0

1. x in quadrant IV means \sin x, so

\cos^2x+\sin^2x=1\implies\sin x=-\sqrt{1-\cos^2x}=-\dfrac{\sqrt3}2

2. x in quadrant I means \cos x>0. Then

\cos x=\sqrt{1-\sin^2x}=\dfrac{\sqrt2}2

3. x in quadrant II means \sin x>0. Then

\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\sqrt{1-\cos^2x}}{-\frac12}=\dfrac{\frac{\sqrt3}2}{-\frac12}=-\sqrt3

4. If \sin x=-1, then \cos x=0, so \tan x is undefined.

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