Precalculus Examples

$\cos (120) \tan (60)$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$- \cos (60) \tan (60)$

Step 2

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 2.1

Add parentheses.

$- (\cos (60) \tan (60))$

Step 2.2

Reorder $\cos (60)$ and $\tan (60)$ .

$- (\tan (60) \cos (60))$

Step 2.3

Rewrite $- \cos (60) \tan (60)$ in terms of sines and cosines.

$- (\frac{\sin (60)}{\cos (60)} \cos (60))$

Step 2.4

Cancel the common factors.

$- \sin (60)$

Step 3

The exact value of $\sin (60)$ is $\frac{\sqrt{3}}{2}$ .

$- \frac{\sqrt{3}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{3}}{2}$

Decimal Form:

$- 0.86602540 \dots$