12.4k views
13 votes
3 sin ^2 x - 3 sin ^4 x =0

User Trask
by
8.3k points

1 Answer

7 votes

I assume you're just solving for x. Factorize the left side as

3 sin²(x) - 3 sin⁴(x) = 3 sin²(x) (1 - sin²(x)) = 0

Recall that

sin²(x) + cos²(x) = 1

so that the equation further reduces to

3 sin²(x) cos²(x) = 0

Also recall the double angle identity,

sin(2x) = 2 sin(x) cos(x)

which lets us rewrite the equation as

3/2² (2 sin(x) cos(x))² = 3/4 sin²(2x) = 0

Solve for x :

3/4 sin²(2x) = 0

sin²(2x) = 0

sin(2x) = 0

2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ

(where n is any integer)

2x = 2nπ or 2x = (2n + 1) π

x = nπ or x = (2n + 1)/2 π

Notice that this means the solution set is

{…, -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 3π, …}

so we can condense the solution further to

x = nπ/2

with any integer n.

User WHOATEMYNOODLES
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories