Question

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

Trigonometric Functions
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) $$\displaystyle{\left(-√{3},{1}\right)}$$

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) $$\displaystyle{\left({1},-\sqrt{{3}}\right)}$$