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26 April, 07:04

Find values for θ that make each statement true (show steps)

1) sinθ = cos (25)

θ =

2) sin (θ/3 + 10) = cos θ

θ =

+5
Answers (1)
  1. 26 April, 07:08
    0
    Step-by-step explanation:

    1. sinФ = cos 25

    25 ° is in the between 0 and 90°

    therefore it can simply represent

    cosФ = sin (90-Ф) = sin (90 - 25) = sin 65

    2. sin (Ф/3 + 10) = cos Ф

    cos Ф = sin (90 - Ф)

    sin (Ф/3 + 10) = cos Ф

    sin (Ф/3 + 10) = cos Ф = sin (90-Ф)

    Ф/3+10=90-Ф

    10 Ф+3/30 = 90-Ф

    10 Ф+3 = 30 (90-Ф)

    10 Ф+3 = 2700-30 Ф

    10 Ф+30 Ф=2700-3

    40 Ф = 2697

    Ф = 2697 / 40 = 67.425 ≅ 67.4°
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