Question

16
for what value of x is \\(\cos(x) = \sin(14^\circ)\\), where \\(0^\circ < x < 90^\circ\\)?

a. \\(28^\circ\\)

b. \\(14^\circ\\)

c. \\(31^\circ\\)

d. \\(76^\circ\\)

Explanation:

Step1: Use co-function identity

Recall $\cos(x) = \sin(90^\circ - x)$

Step2: Set up equation

$\sin(90^\circ - x) = \sin(14^\circ)$

Step3: Solve for x

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

Answer:

D. $76^\circ$