Trigonometry

What you'll learn

• Define sine, cosine, and tangent using right triangle sides
• Solve for missing sides and angles in right triangles using trig ratios
• Understand radian measure and convert between degrees and radians
• Apply basic trig identities: sin²θ + cos²θ = 1, tanθ = sinθ/cosθ
• Apply the Law of Sines (a/sinA = b/sinB = c/sinC) and Law of Cosines (c² = a² + b² − 2ab·cosC) to non-right triangles

Key concepts

SOH-CAH-TOA defines the three main trig ratios: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. These ratios let you find unknown sides or angles in right triangles. Radians are another way to measure angles: 180° = π radians, so to convert, multiply degrees by π/180. The identity sin²θ + cos²θ = 1 is the most important trig identity on the ACT. For non-right triangles, use the Law of Sines: a/sinA = b/sinB = c/sinC (when you know an angle and its opposite side). Use the Law of Cosines: c² = a² + b² − 2ab·cosC (when you know two sides and the included angle, or all three sides). Trigonometry questions make up roughly 7-10% of the Math section (3-4 questions), and they tend to appear in the second half of the test among the harder questions.

Pro tips

• Memorize SOH-CAH-TOA and write it at the top of your scratch paper at the start of the test.
• If a trig question involves a non-right triangle, look for a way to draw an altitude to create right triangles.
• Know the trig values for common angles: sin 30° = 1/2, cos 30° = √3/2, sin 45° = cos 45° = √2/2.