Question

For an acute angle θ, the equation sin (θ) = cos (7°)is true. What is the value of θ?

Answer 1

θ = 83°

Explanation:

For acute angles, the sine of an angle is the cosine of its complement, and vice versa.

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sin(θ) = cos(90° -θ) . . . . relation between sine and cosine

sin(θ) = cos(7°) . . . . . . . . given

90° -θ = 7° . . . . . . . . . matching arguments of cos( )

θ = 83° . . . . . . . . . add θ -7° to both sides