Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.3 - Definition I: Trigonometric Functions - 1.3 Problem Set - Page 32: 28

Answer

The point is $(0,-1)$ $r=1$ $\sin({-90^{\circ}}) =-1$ $\cos({-90}^{\circ}) = 0$ $\tan({-90}^{\circ})$ = undefined
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Work Step by Step

The terminal side of $-90^{\circ}$ in standard position is represented by the blue line in the figure. It lies on the negative $y$ axix. The coordinates of points on the terminal side of $-90^{\circ}$ can be given by $(0,-a)$, where $a$ is a positive number. Choosing $a=1$ arbitrarily, the point is $(0,-1)$. To find the distance from the origin to $(0,-1)$, we use the distance formula $$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(0-0)^2+(-1-0)^2}=1$$ $$\therefore r = \boxed{1}$$ $\sin({-90^{\circ}}) = \dfrac{y}{r} = \dfrac{-1}{1} = \boxed{-1}$ $\cos({-90}^{\circ}) = \dfrac{x}{r} = \dfrac{0}{1} = \boxed{0} $ $\tan({-90}^{\circ}) = \dfrac{y}{x} = \dfrac{-1}{0 } = \fbox{undefined}$
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