Answer: [tex]\begin{gathered} sinθ\text{ = }\frac{21}{29} \\ \\ cosθ\text{ = }\frac{-20}{29} \end{gathered}[/tex]
Explanation:
Given:
The point on the terminal arm is (-20, 21)
To find:
sinθ and cosθ
First we need to determine the distance between the given point and the origin using the formula:
[tex]\begin{gathered} r\text{ = }\sqrt{x^2+y^2} \\ \\ (-20,\text{ 21\rparen: x = -20, y = 21} \\ r\text{ = }\sqrt{(-20)\placeholder{⬚}^2+21^2} \\ r\text{ = }\sqrt{400+441}\text{ = }\sqrt{841} \\ r\text{ = 29} \end{gathered}[/tex]
The trigonometry functions for sinθ and cosθ are determined by:
[tex]\begin{gathered} sinθ\text{ = }\frac{y}{r} \\ cosθ\text{ = }\frac{x}{r} \end{gathered}[/tex][tex]\begin{gathered} sinθ\text{ = }\frac{21}{29} \\ \\ cosθ\text{ = }\frac{-20}{29} \end{gathered}[/tex]
