If sinx=1/5 and x terminates in the first quadrant, determine cos 2x.

Hey there! I'm happy to help!

Let's think of this angle being put inside of a unit circle (a circle with a radius of one). This angle is going to stay inside the first quadrant, so all of its trigonometric ratios will be positive.

We are given that the sin of x is 1/5. To get the x by itself, we can just find the inverse sine of both sides to isolate the x.

x=sin(1/5)

x≈ 11.536959

2x≈ 23.073918

Now, we just cosine this value.

cos2x≈ 0.92

I hope that this helps! Have a wonderful day!