Trigonometry on the SAT is surprisingly predictable. The same patterns repeat every test. Master these 5 shortcuts and you will solve trig questions in under 30 seconds.
Shortcut 1: The Cofunction Identity
If , then .
That is it. The SAT tests this almost every time.
Example 1: Quick Application
If , find .
Done in 15 seconds.
Shortcut 2: Special Triangle Values
Memorize these exact values:
| Angle | |||
|---|---|---|---|
Notice: and (cofunction identity in action!).
Shortcut 3: Draw the Triangle
When you see ", find ":
- Draw a right triangle
- Label: opposite , hypotenuse
- Find adjacent:
Recognize ? Pythagorean triples strike again.
Shortcut 4: The Pythagorean Identity
If : , so .
No triangle drawing needed.
Shortcut 5: Angle of Elevation = Angle of Depression
When the SAT gives you a scenario with someone looking UP at a building and someone on the building looking DOWN, these angles are equal (alternate interior angles with parallel horizontal lines).
This means you only need one triangle, not two.
Common Mistakes to Avoid
- Mixing up opposite and adjacent: "Opposite" and "adjacent" are relative to YOUR angle, not the right angle.
- Forgetting that : If the opposite equals the adjacent, the angle is always .
- Using degrees when the calculator is in radians: Double-check your calculator mode. The SAT uses degrees.
SAT Pro Tip
Trig questions on the SAT are worth the same points as easier algebra questions but take less time IF you know the shortcuts. Spend 5 minutes memorizing the special triangle values and the cofunction identity — it will pay off on every practice test.
Master trigonometry with our Trig Ratios lessons featuring interactive exercises.