Question

1. Find the exact value of sin(195(degrees))

2. If cot2(delta)=5/12 with 0(<or =)2(delta)pi, find cos(delta), sin(delta) , tan(delta).

3.find the exact value of sin2(x) if cos(x)= 4/5. (X is in quadrant 1)

4. Find the exact value of tan2(x) if sin(x)=5/13. ((X) in quadrant 2)

5. Solve sin2(x)+sin(x)=0 for 0<or=x<or=2pi.

6. Write 2sin37(degrees)sin26(degrees) as a sum (or difference).

Answer 1

1.
sin 195°
= - sin15° , by CAST

we know cos 30° = 1 - 2 sin^2 15°
√3/2 = 1 - 2sin^2 15°
2sin^2 15 = 1 - √3/2 = (2-√3)/2
sin^2 15° = (2-√3)/4

sin 15 = √((2-√3)) /2

so sin 195
= -sin15
= -√((2-√3)) /2

3. given cos x = 4/5 , x in I
then by Pythagoras, sinx = 3/5

sin 2x = 2sinx cosx
= 2(3/5)(4/5) = 24/25

5.
sin 2x + sinx = 0 , 0 ≤ x ≤ 2π

2sinxcosx + sinx = 0
sinx(2cosx + 1) = 0
sinx = 0 or cosx = -1/2

x = π/2
x = 3π/2

x = π-π/3 = 2π/3 ---- ( 120°)

Give the others a try, let me know what you got
x = π+π/3 = 4π/3 ---- (240°)

Answer 2

thanks! what do the question marks stand for.

and also CAST?

Answer 3

I will try the others soon.