Precalculus with limits

Question

Use the given conditions to find the exact values of sin(2u), cos(2u) and tan(2u) using the double-angle formulas.

tan(u) = 5/13,    0 < u < 𝜋/2

Answer 1

Since tan(u) is 5/13, that tells us the two legs of a triangle have length 5 and 13. We can use the pythagorean formula to find out the length of the hypotenuse:

√ (13² + 5²) = √194

Now that we know the length of all three sides, we can easily find out sin(u) and cos(u) as well with the trigonometric ratios (or use SOHCAHTOA if you've forgotten them). So we can just plug them into the double angle formulas to find out sin(2u), cos(2u), and tan(2u). Can you finish the problem yourself with this info?