Question

use the diagram to complete the statement.
given △jkl, sin(38°) equals
○ cos(38°).
○ cos(52°).
○ tan(38°).
○ tan(52°).
(diagram of right triangle jkl with right angle at j, angle at k is 52°, angle at l is 38°)

Explanation:

Step1: Recall co-function identity

In a right triangle, \(\sin(\theta)=\cos(90^\circ - \theta)\). For \(\theta = 38^\circ\), \(90^\circ - 38^\circ=52^\circ\). So \(\sin(38^\circ)=\cos(52^\circ)\).

Step2: Check other options

• \(\cos(38^\circ)\) is not equal to \(\sin(38^\circ)\) (unless \(38^\circ = 45^\circ\), which it's not).
• \(\tan(38^\circ)=\frac{\sin(38^\circ)}{\cos(38^\circ)}

eq\sin(38^\circ)\) (unless \(\cos(38^\circ)=1\), which it's not).

• \(\tan(52^\circ)=\frac{\sin(52^\circ)}{\cos(52^\circ)}

eq\sin(38^\circ)\) (since \(\sin(52^\circ)=\cos(38^\circ)\), so this ratio is not equal to \(\sin(38^\circ)\)).

Answer:

\(\cos(52^\circ)\) (the option with \(\cos(52^\circ)\))