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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).

[tex](cos \alpha )^2 + (sin \alpha )^2 =1[/tex]

2) From which you can find:

[tex](cos \alpha )^2 = 1 - (sin \alpha )^2[/tex]

3) Replace sin(α) with 1/4

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

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

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

cos(Θ) = [tex] \sqrt{15} /4[/tex].

And that is the answer.

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