Question

If 3θ is the measure of an acute angle and sin3θ = cos(θ – 26), then find the value of θ.

Answer 1

Given, sin3θ = cos(θ - 26°)

we know , cos(90° - θ) = sinθ

so, sin3θ = cos(90° - 3θ)

now, sin3θ = cos(90° - 3θ) = cos(θ - 26°)

cos(90° - 3θ) = cos(θ - 26°)

90° - 3θ = θ - 26°

4θ = 90° + 26°

4θ = 116°

θ = 29°

hence, value of θ = 29°

Answer 2

Hi ,

Here I am using ' A ' instead of theta .

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Cos ( 90 - A ) = sin A

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It is given that ,

sin 3A = cos ( A - 26 )

cos ( 90 - 3A ) = cos ( A - 26 )

90 - 3A = A - 26

90 + 26 = A + 3A


116 = 4A

A = 116/4

A = 29

I hope this helps you.

: )