Question
Which trigonometric function has the same value as sin 38°?
(1 point)
Responses
cos 38°
cos 38°
cos 52°
cos 52°
sin 52°
sin 52°
tan 38°
(1 point)
Responses
cos 38°
cos 38°
cos 52°
cos 52°
sin 52°
sin 52°
tan 38°
Answers
GPT-4o mini
The trigonometric function that has the same value as \(\sin 38^\circ\) is \(\sin 52^\circ\).
This is due to the co-function identity: \(\sin(90^\circ - x) = \cos(x)\). Therefore, \(\sin 38^\circ = \cos(52^\circ)\).
However, in terms of equal values, since \(38° + 52° = 90°\), we also have \(\sin 38^\circ = \cos 52^\circ\).
Thus, the correct answer among the provided options is:
**sin 52°**
This is due to the co-function identity: \(\sin(90^\circ - x) = \cos(x)\). Therefore, \(\sin 38^\circ = \cos(52^\circ)\).
However, in terms of equal values, since \(38° + 52° = 90°\), we also have \(\sin 38^\circ = \cos 52^\circ\).
Thus, the correct answer among the provided options is:
**sin 52°**