Trigonometry 7th Edition

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

Chapter 1 - Test - Page 51: 19

Answer

Value of $\sin\theta$ will be $\leq 1$, for any angle $\theta$ in standard position as $ \sin\theta$ = $\frac{x}{r}$ and $ x \leq r$

Work Step by Step

For any angle $\theta$ in standard position, let's consider any point P(x,y) on its terminal side. Distance of P from origin, r= $\sqrt {x^{2} + y^{2}}$ Therefore $ r\geq x$ or $ x \leq r$ By definition I, we know that- $ \sin\theta$ = $\frac{x}{r}$ as $ x \leq r$, Hence value of $\frac{x}{r} \leq 1$ or value of $\sin\theta$ will be $\leq 1$, for any angle $\theta$ in standard position.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.