Question

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

Answer 1

Answer:

Choice b is correct answer.

Step-by-step 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.

Answer 2

Answer:

b

Step-by-step explanation:

Using the trigonometric identity

• sin²x + cos²x = 1 , hence

cosx = ± $\sqrt{1-sin^2x}$

cosΦ > 0 for 0 < Φ < $\frac{\pi }{2}$

cosΦ = $\sqrt{1-(\frac{1}{4})^2 }$ = $\sqrt{1-\frac{1}{16} }$ = $\sqrt{\frac{15}{16} }$ = $\frac{\sqrt{15} }{4}$ → b