Trigonometry: Unit Circle & Exact Values
The ACT Math section includes several trigonometry questions testing knowledge beyond basic right-triangle ratios. The unit circle is a circle of radius 1 centered at the origin. Every point on the unit circle has coordinates (cos θ, sin θ), where θ is the angle measured counterclockwise from the positive x-axis. You must memorize the exact values at key angles: at 0°, cos = 1 and sin = 0; at 30°, cos = √3/2 and sin = 1/2; at 45°, cos = sin = √2/2; at 60°, cos = 1/2 and sin = √3/2; at 90°, cos = 0 and sin = 1. The tangent is sin/cos. Understanding the four quadrants is essential: sine is positive in Quadrants I and II; cosine is positive in Quadrants I and IV; tangent is positive in Quadrants I and III. The mnemonic 'All Students Take Calculus' (All, Sine, Tangent, Cosine) identifies which function is positive in each quadrant (I through IV). The ACT also tests reference angles: the acute angle formed between the terminal side of θ and the x-axis, used to find trig values in non-first-quadrant positions.