High school (9–12)
Math
Pre-Calculus: Trigonometry Basics: Standard Practice
Free trigonometry practice for high school pre-calculus. Review right triangle ratios, the unit circle, radian measure, and evaluating sine, cosine, and tangent. Grade-level practice aligned to typical classroom expectations and unit assessments.
Medium Level Guide
Grade-level practice aligned to typical classroom expectations and unit assessments.
Right Triangle Ratios
For angle θ in a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. SOH-CAH-TOA helps remember. Use a calculator for non-special angles in degrees or radians.
Special Right Triangles
A 45-45-90 triangle has legs 1 and hypotenuse √2. A 30-60-90 triangle has sides 1, √3, and 2. These exact values appear on the unit circle and simplify many problems without a calculator.
The Unit Circle
A circle with radius 1 centered at the origin. Each point (x, y) on the circle gives cos θ = x and sin θ = y for angle θ in standard position. Quadrant signs follow ASTC (All Students Take Calculus) mnemonic.
Radians and Applications
π radians equals 180 degrees. Arc length and angular speed use radians. Trigonometry models periodic phenomena like sound waves and seasons. Inverse trig functions find angles from ratios.
FAQ
- Is the unit circle fully memorized here?
- Questions emphasize common angles (0°, 30°, 45°, 60°, 90° and radian equivalents). Full memorization is a classroom goal.
- Does this require a graphing calculator?
- Special angle questions can be done without technology. Other items may use calculator-ready values.