Question

Find the exact value of the expression?
sin a= 24/25, a lies in quadrant 2 and cos B=2/5, B lies in quadrant 1. Find cos(a-b).

Answer 1

Answer on Question #81503 — Math — Trigonometry

Question

Find the exact value of the expression?

sin a = 24/25, a lies in quadrant 2 and cos B = 2/5, B lies in quadrant 1. Find cos(a-b).

Solution

sin(a) = 24/25, a in 2 quadrant.

cos(b) = 2/5, b in 1 quadrant.

cos(a - b) = cos(a)*cos(b) + sin(a)*sin(b)

cos(a) = ±√1 - sin(a)² = ±7/25.

If a lies in 2 quadrant, cos(a) < 0.

cos(a) = -7/25

sin(b) = ±√1 - cos(b)² = ±√21/5. If b lies in 1 quadrant, sin(b) > 0.

sin(b) = √21/5.

cos(a - b) = cos(a)*cos(b) + sin(a)*sin(b) = -2/5 * 7/25 + 24/25 * √21/5 = 24√21 - 14/625

Answer: 24√21 - 14/625.

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