Pre calculus exact value?

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

1 Answer

Relevance
  • tc
    Lv 7
    7 years ago

    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

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