SAT Trigonometry & Right Triangles

Trigonometry questions appear 2–3 times per SAT and focus on right triangle trig (SOH-CAH-TOA), special right triangles, and radian measure. You'll find missing sides or angles using sine, cosine, and tangent, and apply the Pythagorean theorem.

The SAT tests the co-function identity (sin x = cos(90°−x)) and the two special triangles: 30-60-90 (sides 1-√3-2) and 45-45-90 (sides 1-1-√2). You won't need the law of sines, law of cosines, or advanced trig identities.

SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. Always label the sides relative to the specific angle you're working with — opposite and adjacent switch depending on which angle you choose.

Special triangles: 30-60-90 has sides in ratio 1:√3:2; 45-45-90 has sides in ratio 1:1:√2. Memorize these ratios — they appear on nearly every SAT and are faster than the calculator.

Co-function identity: sin(x) = cos(90°−x). Two angles adding to 90° have swapped sine and cosine values.

Labeling opposite and adjacent from the wrong angle. Always mark the reference angle on the diagram before labeling the sides — this single step prevents the most common trig error.

Forgetting to take the square root after the Pythagorean theorem. a² + b² = c² gives c², not c. The hypotenuse is √(a²+b²).

Mixing up sin(30°) = 1/2 and sin(60°) = √3/2. Associate 30° with the smaller value (1/2) and 60° with the larger value (√3/2).

Draw and label the right triangle for every trig problem — even when you think you can visualize it. Label the hypotenuse, opposite side, and adjacent side from the reference angle before writing any formula.

ScoreBooster's Geometry topic includes trig problems with step-by-step solution breakdowns that show exactly where students typically make labeling errors.