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Leya [2.2K]
3 years ago
15

Given that sin theta = 1/4, 0

Mathematics
1 answer:
GaryK [48]3 years ago
6 0
Answer: cos(Θ) = (√15) / 4

Explanation:

The question states:

1) sin(Θ) = 1/4

2) 0 < Θ < π / 2

3) find cos(Θ)

This is how you solve it.

1) Use the fundamental identity (in this part I use α instead of Θ, just for facility of wirting the symbols, but they mean the same for the case).

(cos \alpha )^2 + (sin \alpha )^2 =1

2) From which you can find:

(cos \alpha )^2 = 1 - (sin \alpha )^2

3) Replace sin(α) with 1/4

=> (cos \alpha )^2 = 1 - (1/4)^2 = 1 - 1/16 = 15/16

=> cos \alpha =+/- \sqrt{15/16} = +/- (\sqrt{15} )/4

4) Given that the angle is in the first quadrant, you know that cosine is positive and the final answer is:

cos(Θ) = \sqrt{15} /4.

And that is the answer.
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