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

`\cos(\theta_1) = (√(111))/(20)`

Explanation:

Given

`\sin(\theta_1) = (17)/(20)`

`Quadrant = 1`

Required

`\cos(\theta_1)`

We know that:

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

This implies that:

`((17)/(20))^2 + \cos^2(\theta_1) = 1`

Collect like terms

`\cos^2(\theta_1) = 1 -((17)/(20))^2`

`\cos^2(\theta_1) = 1 -(289)/(400)`

Take LCM and solve

`\cos^2(\theta_1) = (400 -289)/(400)`

`\cos^2(\theta_1) = (111)/(400)`

Take square roots

`\cos(\theta_1) = (√(111))/(√(400))`

`\cos(\theta_1) = (√(111))/(20)`