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: 29

Answer

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

The terminal side of $0^{\circ}$ in standard position is represented by the blue line in the figure. It lies on the positive $x$ axix. The coordinates of points on the terminal side of $0^{\circ}$ 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 $$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(1-0)^2+(0-0)^2}=1$$ $$\therefore r = \boxed{1}$$ $\sin({0^{\circ}}) = \dfrac{y}{r} = \dfrac{0}{1} = \boxed{0}$ $\cos({0}^{\circ}) = \dfrac{x}{r} = \dfrac{1}{1} = \boxed{1} $ $\tan({0}^{\circ}) = \dfrac{y}{x} = \dfrac{0}{1 } = \boxed{0}$
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