Geometry & Trigonometry Medium
⏱ 10 min 📊 Medium ⭐ Premium

Complementary Angle Relationship (sin/cos)

Understand and apply the relationship sin(x) = cos(90° - x).

Theory

The Cofunction Identity

For any acute angle x: [formula] This is because in a right triangle, the two acute angles are complementary (x + (90° - x) = 90°), and the side opposite one angle is adjacent to the other. In radians: sin(theta) = cos(frac{pi}{2} - theta)

Example: If sin(25°) = 0.4226, what is cos(65°)?

Summary

SAT Pro Tip

The SAT loves this identity! If you see sin(x°) = cos(y°), then x + y = 90. This is tested almost every time and is a quick 30-second solve.

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