Trigonometry Examples

$4 \sin (60) - 3 \tan (135)$

Step 1

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

$4 \frac{\sqrt{3}}{2} - 3 \tan (135)$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $4$ .

$2 (2) \frac{\sqrt{3}}{2} - 3 \tan (135)$

Step 2.2

Cancel the common factor.

$2 \cdot 2 \frac{\sqrt{3}}{2} - 3 \tan (135)$

Step 2.3

Rewrite the expression.

$2 \sqrt{3} - 3 \tan (135)$

Step 3

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

$2 \sqrt{3} - 3 (- \tan (45))$

Step 4

The exact value of $\tan (45)$ is $1$ .

$2 \sqrt{3} - 3 (- 1 \cdot 1)$

Step 5

Multiply $- 3 (- 1 \cdot 1)$ .

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Step 5.1

Multiply $- 1$ by $1$ .

$2 \sqrt{3} - 3 \cdot - 1$

Step 5.2

Multiply $- 3$ by $- 1$ .

$2 \sqrt{3} + 3$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3} + 3$

Decimal Form:

$6.46410161 \dots$