To determine which of the options is NOT equivalent to \(\cos 240^\circ\), we first need to calculate \(\cos 240^\circ\).
Since \(240^\circ\) is in the third quadrant, we can find its reference angle: \[ 240^\circ - 180^\circ = 60^\circ \] In the third quadrant, the cosine function is negative, so: \[ \cos 240^\circ = -\cos 60^\circ = -\frac{1}{2} \]
Now, we will evaluate each option:
A) \(\cos 120^\circ\): \[ \cos 120^\circ = -\cos 60^\circ = -\frac{1}{2} \]
B) \(-\sin 150^\circ\): \[ \sin 150^\circ = \sin(180^\circ - 30^\circ) = \sin 30^\circ = \frac{1}{2} \] So, \[ -\sin 150^\circ = -\frac{1}{2} \]
C) \(-\sin 210^\circ\): \[ \sin 210^\circ = -\sin 30^\circ = -\frac{1}{2} \] So, \[ -\sin 210^\circ = -(-\frac{1}{2}) = \frac{1}{2} \]
D) \(\sin 330^\circ\): \[ \sin 330^\circ = -\sin 30^\circ = -\frac{1}{2} \]
Now, we summarize the values:
- \(\cos 120^\circ = -\frac{1}{2}\) (equivalent)
- \(-\sin 150^\circ = -\frac{1}{2}\) (equivalent)
- \(-\sin 210^\circ = \frac{1}{2}\) (not equivalent)
- \(\sin 330^\circ = -\frac{1}{2}\) (equivalent)
The option that is NOT equivalent to \(\cos 240^\circ\) is:
C) -\sin 210°