Question

Given that sin∅ = 1/4, 0 < ∅ < π/2, what is the exact value of cos∅?

a. (√4)/4
b. (√15)/4
c. (4π)/2
d. (4√2)/4

Answer 1

b

Explanation:

Using the trigonometric identity

• sin²x + cos²x = 1 , hence

cosx = ±
`√(1-sin^2x)`

cosΦ > 0 for 0 < Φ <
`(\pi )/(2)`

cosΦ =
`\sqrt{1-((1)/(4))^2 }` =
`\sqrt{1-(1)/(16) }` =
`\sqrt{(15)/(16) }` =
`(√(15) )/(4)` → b

Answer 2

Choice b is correct answer.

Explanation:

We have to find the value of cos∅x where the value of sin∅ is given.

Given that

sin∅ = 1/4

We use trigonometric identity to solve this question.

Trigonometric identity:

sin²∅+cos²∅=1

Separating cos²∅

cos²∅= 1-sin²∅

Taking square root to above equation

cos∅=√1-sin²∅

cos∅=√1-(sin∅)²

Putting the given value of sin∅,we get

cos∅= √1-(1/4)²

cos∅= √1-1/16

cos∅=√16-1/16

cos∅= √15/16

cos∅= (√15)/4

Hence, the answer is Choice b.