Overview
This lecture covers SAT trigonometry questions, focusing on two key types: SOHCAHTOA and the complementary angle (complementary rule) identities. Mastery of these types ensures you can solve any trigonometry question on the SAT.
Identifying Trigonometry Questions
- Trigonometry questions involve the terms sine (sin) or cosine (cos).
- If you see "sin" or "cos" in a question, it's trigonometry.
SOHCAHTOA Type Questions
- SOHCAHTOA is a mnemonic for remembering trig ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse.
- Sine of angle X: sin(X) = opposite side / hypotenuse.
- Cosine of angle Y: cos(Y) = adjacent side / hypotenuse.
- Always convert decimals (like 0.6) to fractions for easier triangle visualization (e.g., 0.6 = 3/5).
Complementary Rule Type Questions
- The complementary rule: sin(X) = cos(90°−X) and cos(X) = sin(90°−X).
- Use the complementary rule when you see both sine and cosine or an angle like "90−X" in the question.
- The two non-right angles in a right triangle always add up to 90°.
Examples from the Lecture
- If sin(X) = 0.6, rewrite as 3/5, so opposite = 3, hypotenuse = 5.
- cos(Y) in the same triangle is 3/5 (adjacent to Y / hypotenuse).
- If sin(X) = 4/5, then cos(90°−X) = 4/5 by the complementary rule.
Key Terms & Definitions
- SOHCAHTOA — Mnemonic for trigonometric ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
- Complementary Rule — Identity that links sine and cosine of complementary angles: sin(X) = cos(90°−X).
- Hypotenuse — The longest side of a right triangle, opposite the right angle.
- Opposite/Adjacent Sides — Relative to the angle in question, "opposite" is across from the angle, "adjacent" is next to it.
Action Items / Next Steps
- Download and complete the trigonometry worksheet for additional SAT practice.
- Watch the in-depth trigonometry lecture (link provided in original content).
- Review SOHCAHTOA and complementary rule identities until you can recall and apply them quickly.