Question

for what value of x is cos(x) = sin(14°), where 0° < x < 90°?
a. 28°
b. 76°
c. 31°
d. 14°

Explanation:

Step1: Use the co - function identity

The co - function identity states that \(\cos\theta=\sin(90^{\circ}-\theta)\).
If \(\cos(x)=\sin(14^{\circ})\), then by the co - function identity \(\sin(90^{\circ}-x)=\sin(14^{\circ})\).

Step2: Solve for \(x\)

Since \(y = \sin\alpha\) is a one - to - one function for \(0^{\circ}\lt\alpha\lt90^{\circ}\), if \(\sin(90^{\circ}-x)=\sin(14^{\circ})\), then \(90^{\circ}-x = 14^{\circ}\).

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Answer:

B. \(76^{\circ}\)