Pre calculus exact value?

Question

Need help for my pre calc final.

How do you solve these?

Find the exact value for the following:

1) sin 315^degree symbol

2) sec ( 22 pie / 3)

Evaluate the following:

1) log3 1/2

2) log4 8

3) log9 radical 3

Answer 1

1) sin 315° => reference angle 45°

=-1/√2 = -√2/2

2) sec ( 22 pie / 3) = sec(7 1/3 π) = sec(4π/3) = sec(240°)

=> reference angle 60°

sec(240°) = 1/cos240° = -2

1) log₃ 1/2 = -0.631 => by calculator

2) log₂ 8 = x

2^x = 8 = 2^3

x = 3

3) log₉√3 = x

9^x = √3

(3^2)^x = 3^(1/2)

3^2x = 3^(1/2)

2x = 1/2

x = 1/4