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.
