Trig Identities Summer School Day 2

In problems 35 - 38, verify the identity. 35. sin x csc x = 1

36.

cot2x(sec2x - 1) = 1

37.

38.

1 sin x

cos x + sin x tan x = sec x

Title: Jul 21­7:28 AM (1 of 8)

sin x = cos2x sin x

Find the exact value of the trigonometric function given that sin u = -7/25 and cos v = -4/5. (Both u and v are in Quadrant III.) 7. cos(u + v) 8. sec(v - u)

9.

csc(u + v)

Title: Jul 21­7:29 AM (2 of 8)

10.

sin(v - u)

Verify the identity. 11. sin(x + y)sin(x - y) = sin2x - sin2y

Title: Jul 21­7:30 AM (3 of 8)

12.

sin(x + y) + sin(x - y) = 2 sin x cos y

Verify the identity.

Title: Jul 21­7:31 AM (4 of 8)

Title: Jul 21­7:32 AM (5 of 8)

Title: Jul 21­7:32 AM (6 of 8)

Title: Jul 21­7:33 AM (7 of 8)

Find the exact value of the trigonometric function given that sin u = -12/13 and cos v = -4/5. (u is in Quadrant IV and v is in Quadrant II.) 1. cos(2u) 2. sin(2v)

3. cos(v/2)

Title: Jul 22­7:26 AM (8 of 8)

4. sin(u/2)