Question

If SinA=3/5, find the value of Sin2A and Cos2A.

A) Sin2A = 24/25, Cos2A = 7/25
B) Sin2A = 16/25, Cos2A = 9/25
C) Sin2A = 9/25, Cos2A = 16/25
D) Sin2A = 7/25, Cos2A = 24/25

Answer 1

Using the double-angle formulas for sine and cosine with the provided SinA value, we determine Sin2A to be 24/25 and Cos2A to be 7/25.

Step-by-step explanation:

Given that SinA = 3/5, to find Sin2A and Cos2A, we can use the double-angle formulas for sine and cosine. The formula for Sin2A is 2SinACosA and for Cos2A we have two formulas: Cos2A - Sin2A or 1 - 2Sin2A. First, we need to find CosA, which can be determined by using the Pythagorean Theorem for a right triangle (since Sin2A + Cos2A = 1). As SinA = 3/5, CosA can be found by taking the square root of (1 - Sin2A), which gives us CosA = 4/5.

We then apply the double-angle formulas:

• Sin2A = 2 * 3/5 * 4/5 = 24/25
• Cos2A = Cos2A - Sin2A = (4/5)2 - (3/5)2 = 16/25 - 9/25 = 7/25

Therefore, the correct answer is A) Sin2A = 24/25, Cos2A = 7/25.