Finite Math Examples

$\cos (180) \cdot {(\sin (135) \cdot \tan (30) - \cos (135))}^{22} \cdot (2 P^{3})$

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.

$- \cos (0) \cdot {(\sin (135) \cdot \tan (30) - \cos (135))}^{22} \cdot (2 P^{3})$

Step 2

The exact value of $\cos (0)$ is $1$ .

$- 1 \cdot 1 \cdot {(\sin (135) \cdot \tan (30) - \cos (135))}^{22} \cdot (2 P^{3})$

Step 3

Multiply $- 1$ by $1$ .

$- 1 \cdot {(\sin (135) \cdot \tan (30) - \cos (135))}^{22} \cdot (2 P^{3})$

Step 4

Simplify each term.

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Step 4.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$- 1 \cdot {(\sin (45) \cdot \tan (30) - \cos (135))}^{22} \cdot (2 P^{3})$

Step 4.2

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$- 1 \cdot {(\frac{\sqrt{2}}{2} \cdot \tan (30) - \cos (135))}^{22} \cdot (2 P^{3})$

Step 4.3

The exact value of $\tan (30)$ is $\frac{\sqrt{3}}{3}$ .

$- 1 \cdot {(\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{3} - \cos (135))}^{22} \cdot (2 P^{3})$

Step 4.4

Multiply $\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{3}$ .

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Step 4.4.1

Multiply $\frac{\sqrt{2}}{2}$ by $\frac{\sqrt{3}}{3}$ .

$- 1 \cdot {(\frac{\sqrt{2} \sqrt{3}}{2 \cdot 3} - \cos (135))}^{22} \cdot (2 P^{3})$

Step 4.4.2

Combine using the product rule for radicals.

$- 1 \cdot {(\frac{\sqrt{2 \cdot 3}}{2 \cdot 3} - \cos (135))}^{22} \cdot (2 P^{3})$

Step 4.4.3

Multiply $2$ by $3$ .

$- 1 \cdot {(\frac{\sqrt{6}}{2 \cdot 3} - \cos (135))}^{22} \cdot (2 P^{3})$

Step 4.4.4

Multiply $2$ by $3$ .

$- 1 \cdot {(\frac{\sqrt{6}}{6} - \cos (135))}^{22} \cdot (2 P^{3})$

Step 4.5

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.

$- 1 \cdot {(\frac{\sqrt{6}}{6} - - \cos (45))}^{22} \cdot (2 P^{3})$

Step 4.6

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

$- 1 \cdot {(\frac{\sqrt{6}}{6} - - \frac{\sqrt{2}}{2})}^{22} \cdot (2 P^{3})$

Step 4.7

Multiply $- - \frac{\sqrt{2}}{2}$ .

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Step 4.7.1

Multiply $- 1$ by $- 1$ .

$- 1 \cdot {(\frac{\sqrt{6}}{6} + 1 \frac{\sqrt{2}}{2})}^{22} \cdot (2 P^{3})$

Step 4.7.2

Multiply $\frac{\sqrt{2}}{2}$ by $1$ .

$- 1 \cdot {(\frac{\sqrt{6}}{6} + \frac{\sqrt{2}}{2})}^{22} \cdot (2 P^{3})$

Step 5

Simplify the expression.

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Step 5.1

Rewrite $- 1 {(\frac{\sqrt{6}}{6} + \frac{\sqrt{2}}{2})}^{22}$ as $- {(\frac{\sqrt{6}}{6} + \frac{\sqrt{2}}{2})}^{22}$ .

$- {(\frac{\sqrt{6}}{6} + \frac{\sqrt{2}}{2})}^{22} \cdot (2 P^{3})$

Step 5.2

Multiply $2$ by $- 1$ .

$- 2 {(\frac{\sqrt{6}}{6} + \frac{\sqrt{2}}{2})}^{22} P^{3}$