If [tex]\sin \Theta = \frac{7}{25}[/tex], use the Pythagorean Identity to find [tex]\cos \Theta[/tex].

SinƟ = 7/25 so to get Ɵ, just do inverse Sin (Sin^-1) of 7/25 to get Ɵ. Then put the value of Ɵ into Cos. With numbers: Ɵ = Sin^-1(7/25) = 16.26 CosƟ = Cos(16.26) = 0.96

Answered by lburke | 2024-06-10

It might be a good idea to sketch out a triangle to help you answer this question.
You know that sin = opposite over hypotenuse, which means the opposite side of the triangle has length 7 and the hypotenuse has length 25 (this could be simplified, for example the triangle could actually have sides length 14 and 50, 21 and 75, etc, but as it cancels this is unimportant).
Using Pythagoras' theorem, you can work out the adjacent side: A = 2 5 2 − 7 2 ​ = 625 − 49 ​ = 576 ​ = 24
As cos = adjacent over hypotenuse, you know that cosθ = 24/25

Answered by superkoopasirf | 2024-06-24

To find cos Θ given sin Θ = 25 7 ​ , we use the Pythagorean Identity. This leads us to the result cos Θ = 25 24 ​ if Θ is in the first quadrant. Thus, the cosine value of the angle is 25 24 ​ .
;

Answered by superkoopasirf | 2024-08-14