SAT Math: Basic Trigonometric Identities
16+ practice questions in Praczo
The concept, explained
- 1
The most freqently tested identity on the SAT is the Complementary Angle Theorem: sin(x) = cos(90° - x) or sin(x) = cos(π/2 - x).
- 2
This means if two angles add up to 90 degrees, the sine of one equals the cosine of the other (e.g., sin 30° = cos 60°).
- 3
Tangent is sine divided by cosine: tan(x) = sin(x) / cos(x).
- 4
Pythagorean identify: sin²(x) + cos²(x) = 1.
- 5
If given a right triangle and told sin(A) = 3/5, you automatically know cos(B) = 3/5, assuming A and B are the acute angles.
- ✗ Confusing the complementary angle rule with supplementary angles.
- ✗ Thinking sin(x) could equal cos(x) for all x (it's only true for x = 45°).
SAT-style practice
In a right triangle, the acute angles are A and B. If sin(A) = 0.8, what is the value of cos(B)?
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