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: 26

Answer

The point is $(-1,0)$ $r=1$ $\sin{180^{\circ}} =0$ $\cos{180}^{\circ} =-1$ $\tan{180}^{\circ} = 0$
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Work Step by Step

The terminal side of $180^{\circ}$ in standard position is represented by the blue line in the figure. It lies on the negative $x$ axis. The coordinates of points on the terminal side of $180^{\circ}$ can be given by $(-a,0)$, where $a$ is a positive number. Choosing $a=1$ arbitrarily, the point is $(-1,0)$. To find the distance from the origin to $(-1,0)$, we use the distance formula $$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(-1-0)^2+(0-0)^2}=1$$ $$\therefore r = \boxed{1}$$ $\sin{180^{\circ}} = \dfrac{y}{r} = \dfrac{0}{1} = \boxed{0}$ $\cos{180}^{\circ} = \dfrac{x}{r} = \dfrac{-1}{1} = \boxed{-1} $ $\tan{180}^{\circ} = \dfrac{y}{x} = \dfrac{0}{-1 } = \boxed{0}$
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