If sin(x) = /45 and cos(y) = 5/13 with both x and y terminating in quadrant 1 find the exact value of cos(x-y)
cos(4/5 - 5/13)
Is this what I would do?
3 answers
Your sin(x) fraction lacks a numerator
the sine is 4/5 sorry!
No, that is not what you would do. Call the angles A and B.
For the angles you have chosen,
cos(x) = 3/5 and sin(y) = 12/13. You can prove that with the Pythagorean theorem, or sin^2 + cos^2 = 1. That will make the calculation easier.
Then use the identity:
cos(A-B) = cosA cosB + sinA sin B
= (3/5)(5/13) + (4/5)(12/13)
= (15 + 48)/65 = 63/65
For the angles you have chosen,
cos(x) = 3/5 and sin(y) = 12/13. You can prove that with the Pythagorean theorem, or sin^2 + cos^2 = 1. That will make the calculation easier.
Then use the identity:
cos(A-B) = cosA cosB + sinA sin B
= (3/5)(5/13) + (4/5)(12/13)
= (15 + 48)/65 = 63/65
1 answer