Question
Which trigonometric function has the same value as sin 75°?
(1 point)
Responses
cos 75°
cos 75 °
cos 15°
cos 15 °
sin 15°
sin 15 °
tan 75°
(1 point)
Responses
cos 75°
cos 75 °
cos 15°
cos 15 °
sin 15°
sin 15 °
tan 75°
Answers
GPT-4o mini
To find which trigonometric function has the same value as \( \sin 75^\circ \), we can use the following trigonometric identity:
\[
\sin(90^\circ - x) = \cos(x)
\]
In this case, we can set \( x = 15^\circ \):
\[
\sin(75^\circ) = \sin(90^\circ - 15^\circ) = \cos(15^\circ)
\]
Therefore, the correct answer is:
**cos 15°**
\[
\sin(90^\circ - x) = \cos(x)
\]
In this case, we can set \( x = 15^\circ \):
\[
\sin(75^\circ) = \sin(90^\circ - 15^\circ) = \cos(15^\circ)
\]
Therefore, the correct answer is:
**cos 15°**