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Verdich [7]
3 years ago
12

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

Mathematics
2 answers:
salantis [7]3 years ago
8 0

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.



Artemon [7]3 years ago
3 0

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


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