If csc(Theta) = 1 (1)/(4), then cos(theta) = ?

Question

If csc(Theta) = 1
`(1)/(4)`, then cos(theta) = ?

Answer 1

+/- 3/5

Explanation:

`\text{csc}(\theta)` = 1 1/4 Convert 1 1/4 into an improper fraction

`\text{csc}(\theta)=(5)/(4)` Turn 5/4 upsidedown to get sin( sin
`\theta`)

`(1)/(csc(\theta)) =sin(\theta)\\` 1 / csc(theta) = sin(theta)

`sin(\theta) = 4/5` sin(theta) = 4/5 which is the reciprocal of 5/4

Cos(theta) = sqrt(1 - sin^2(theta) ) This is the identity relationship between sin(theta) and cos(theta)

Cos(theta) = sqrt( 1 - (4/5)^2 ) (4/5)^2 = 16/25; 1 - 16/25 = 9/25

Cos(theta) = sqrt( 9/25)

Cos(theta) = +/- sqrt(9/25) sqrt of 9/25 = 3/5

cos(theta) = +/- 3/5 Answer <<<<