Question

The angle \theta_1θ 1 ​ theta, start subscript, 1, end subscript is located in Quadrant \text{I}Istart text, I, end text, and \sin(\theta_1)=\dfrac{17}{20}sin(θ 1 ​ )= 20 17 ​ sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 17, divided by, 20, end fraction .

Answer 1

Answer:

$\cos(\theta_1) = \frac{\sqrt{111}}{20}$

Step-by-step explanation:

Given

$\sin(\theta_1) = \frac{17}{20}$

$Quadrant = 1$

Required

$\cos(\theta_1)$

We know that:

$\sin^2(\theta_1) + \cos^2(\theta_1) = 1$

This implies that:

$(\frac{17}{20})^2 + \cos^2(\theta_1) = 1$

Collect like terms

$\cos^2(\theta_1) = 1 -(\frac{17}{20})^2$

$\cos^2(\theta_1) = 1 -\frac{289}{400}$

Take LCM and solve

$\cos^2(\theta_1) = \frac{400 -289}{400}$

$\cos^2(\theta_1) = \frac{111}{400}$

Take square roots

$\cos(\theta_1) = \frac{\sqrt{111}}{\sqrt{400}}$

$\cos(\theta_1) = \frac{\sqrt{111}}{20}$