If q is between 0º and 90º and tan (theta) = 7/8 find cos (theta)

Question

Mathematics

Reese Thornton

30 May, 23:59

If q is between 0º and 90º and tan (theta) = 7/8 find cos (theta)

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Answers (1)

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Ward · Answer 1

8/√113

Step-by-step explanation:

0< θ < 90 degree; tan (θ) = 7/8 find cos (θ)

Using the identity

1 + tan²θ = sec²θ (where sec θ = 1/cosθ)

cosθ = √{1 / (1 + tan²θ) } = √{ 1 / (1 + (7/8) ²} = √{ 1 / (1 + 49/64) }

= √{ 64/113} = 8/√113