Question

40 POINTS !!!!!PLEASE HELPPP!!!!!!

Answer 1

cos(theta) = 3sqrt(58)/58

sin(theta) = 7sqrt(58)/58

Explanation:

Cos(2theta) = 2cos²(theta) - 1

-20/29 = 2cos²(theta) - 1

2cos²(theta) = 9/29

cos²(theta) = 9/58

cos(theta) = sqrt(9/58)

cos(theta) = 3sqrt(58)/58

sin²(theta) = 1 - cos²(theta)

sin²(theta) = 1 - 9/58

sin²(theta) = 49/58

sin(theta) = sqrt(49/58)

sin(theta) = 7sqrt(58)/58

sqrt: square root

Answer 2

sin(a) =
`(7√(5) )/(20)`

Explanation:

cos(2a) = cos²(a)-sin²(a) = [1-sin²(a)]-sin²(a)= 1 - 2sin²(a)

1 - 2sin²(a) = -20/29

- 2sin²(a) = -49/40

sin²(a) = 49/80

sin(a) =
`\sqrt{(49)/(80) }`

sin(a) =
`(√(49) √(80) )/(80)` =
`(7*4√(5) )/(80)`

sin(a) =
`(7√(5) )/(20)`