Question

Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. sin(u) = −4/5, 3/2 < u < 2

Answer 1

The exact values of sin(2u), cos(2u), and tan(2u) are -96/125, -33/25, and 288/165, respectively.

Step-by-step explanation:

To find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas, we need to use the given conditions sin(u) = -4/5 and 3/2 < u < 2.

The double-angle formulas are:

• sin(2u) = 2sin(u)cos(u)
• cos(2u) = cos²(u) - sin²(u)
• tan(2u) = sin(2u) / cos(2u)

Substituting sin(u) = -4/5 into the double-angle formulas, we can calculate:

• sin(2u) = 2(-4/5)(√(1 - (-4/5)²)) = -96/125
• cos(2u) = (√(1 - (-4/5)²))² - (-4/5)² = -33/25
• tan(2u) = -96/125 / (-33/25) = 288/165