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.
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.
The highlighted points show every angle that makes the equation true.
Get the trig expression alone: sin(x) = value, cos(x) = value, or tan(x) = value.
Ignore the sign at first. Ask: what special angle has this sine, cosine, or tangent value?
Sine is y, cosine is x, tangent is y/x. Positive or negative tells you where the answers live.
Quadrant I: all positive. Quadrant II: sine positive. Quadrant III: tangent positive. Quadrant IV: cosine positive.
Type answers as degrees separated by commas. Example: 30, 150