Question

Solve the equation in degrees for all exact solutions where appropriate. Round approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.

Answer 1

The equation is an illustration of trigonometry ratios, and the non-negative values of x are 30 and 270 degrees

How to solve the equation?

The equation is given as:

2sin²(x) + sin(x) = 1

Let y = sin(x)

So, the equation becomes

2y² + y = 1

Rewrite as:

2y² + y - 1 = 0

Expand

2y² + 2y - y - 1 = 0

Factorize

2y(y + 1) - 1(y + 1) = 0

Expand

(2y - 1)(y + 1) = 0

Split

2y - 1 = 0 or y + 1 = 0

Solve for y

y = 0.5 or y = -1

Recall that: y = sin(x)

So, we have:

sin(x) = 0.5 and sin(x) = -1

Take the arcsin of both sides

x = sin⁻¹(0.5) and x = sin⁻¹(-1)

x = 30 degrees and x = 270

Hence, the non-negative values of x are 30 and 270 degrees

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