Question

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

Explanation:

Step1: Use co - function identity

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

Step2: Calculate the value of \(x\)

$$x=90^{\circ}-14^{\circ}$$

$$x = 76^{\circ}$$

Answer:

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