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: 25

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 positive $y$ axis. 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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