If sinA = 1/2, find the value of sin3A

Question

Can someone pls help me to solve this? I just know that sin2A = 2sinA.cosA, but it doesn't seem like that formula is helpful in this question. I have no idea about what to do for sin3A.

Answer

For this question, we need to use the formula of sin3A = 3sinA - 4sin³A

If it was cos3A, the formula would be 4cos³A - 3cosA

So in this question, we have given sinA = 1/2. Let's use it in the formula of sin3A

sin3A = 3sinA - 4sin³A = 3( $\frac 12$ ) - 4( $\frac{1}{8}$ ) = $\frac 32$ - $\frac 12$ = 1

The answer is 1.

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