MrWittman.com • algebra 2 / precalculus

Solving Trig Equations

Turn equations like sin(x) = 1/2, cos(x) = -√2/2, and tan(x) = √3 into quadrant decisions. Pick an equation, watch the unit circle highlight the answers, then practice until the pattern feels automatic.

Reference angles
Quadrant logic
0° ≤ x < 360°
Sine • Cosine • Tangent

Equation Explorer

Choose a function and exact value. The tool shows the reference angle, the quadrants that work, and the full solution set for one trip around the circle.

Solve on 0° ≤ x < 360°

    Unit Circle View

    The highlighted points show every angle that makes the equation true.

    The 4-Step Game Plan

    1Isolate trig

    Get the trig expression alone: sin(x) = value, cos(x) = value, or tan(x) = value.

    2Find the reference angle

    Ignore the sign at first. Ask: what special angle has this sine, cosine, or tangent value?

    3Use the sign to pick quadrants

    Sine is y, cosine is x, tangent is y/x. Positive or negative tells you where the answers live.

    ASTC
    All Students Take Calculus

    Quadrant I: all positive. Quadrant II: sine positive. Quadrant III: tangent positive. Quadrant IV: cosine positive.

    Quick Practice

    Type answers as degrees separated by commas. Example: 30, 150