Geometry and TrigonometryVery hardComplementary angle trig identity (sin/cos)
Geometry and Trigonometry practice question
In a right triangle, angles A and B are the two acute angles, so A + B = 90°. If sin A = 0.6, what is the value of cos B?
Answer: 0.6 or .6 or 3/5
For complementary angles, cos B = cos(90° − A) = sin A. Since A + B = 90°, cos B = sin A = 0.6. The trap is computing cos A (which is 0.8 here) instead of using the complementary-angle identity to get cos B.
Common wrong answers
- If you answered 0.8
- 0.8 is cos A, found from sin²A + cos²A = 1 — but the question asks for cos B, and since B = 90° − A, cos B equals sin A = 0.6.
- If you answered 0.4
- Subtracting 0.6 from 1 isn't how complementary angles work; the identity is cos(90° − A) = sin A, so cos B = 0.6.
- If you answered 0.75
- That's tan A = 0.6/0.8. The complementary-angle identity gives cos B = cos(90° − A) = sin A = 0.6 directly.
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