Question

Select the point on the terminal side of 0. 0 = -60°, (a) (-1,-1) (b) ( 1, -sqrt3)

Trigonometric Functions
ANSWERED
asked 2021-09-12
Select the point on the terminal side of 0.
\(\displaystyle{0}=-{60}°\)
(a) \(\displaystyle{\left(-{1},-{1}\right)}\)
(b) \(\displaystyle{\left({1},-√{3}\right)}\)
(c) \(\displaystyle{\left(-√{3},{1}\right)}\)

Expert Answers (1)

2021-09-13
As we know from the Trigonometric functions
\(\displaystyle{\tan{\theta}}=\frac{{y}}{{x}}\)
\(\displaystyle{\tan{-}}{60}^{\circ}=\frac{{y}}{{x}}\)
\(\displaystyle-\sqrt{{3}}=\frac{{y}}{{x}}\)
Now check the points whose \(\displaystyle\frac{{y}}{{x}}\) value is equal to \(\displaystyle-\sqrt{{3}}\). Than we cansay that the point is on the terminal side of theta.
a) For the point (-1,-1)
b) For the point \(\displaystyle{\left({1},-\sqrt{{3}}\right)}\)
\(\displaystyle\frac{{y}}{{x}}=\frac{{-\sqrt{{3}}}}{{1}}=-\sqrt{{3}}\)
c) For the point \(\displaystyle{\left(-\sqrt{{3}},{1}\right)}\)
\(\displaystyle\frac{{y}}{{x}}=\frac{{1}}{{-\sqrt{{3}}}}=-\frac{{1}}{\sqrt{{3}}}\)
So the point b is the terminal side of theta.
Result : B) \(\displaystyle{\left({1},-\sqrt{{3}}\right)}\)
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