Trigonometry Examples

$\frac{2 \cos (156) (\sin^{2} (150))}{\cos (336)}$

Step 1

Separate fractions.

$\frac{2 (\sin^{2} (150))}{1} \cdot \frac{\cos (156)}{\cos (336)}$

Step 2

Rewrite $\frac{\cos (156)}{\cos (336)}$ as a product.

$\frac{2 (\sin^{2} (150))}{1} (\cos (156) \frac{1}{\cos (336)})$

Step 3

Write $\cos (156)$ as a fraction with denominator $1$ .

$\frac{2 (\sin^{2} (150))}{1} (\frac{\cos (156)}{1} \cdot \frac{1}{\cos (336)})$

Step 4

Simplify.

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Step 4.1

Divide $\cos (156)$ by $1$ .

$\frac{2 (\sin^{2} (150))}{1} (\cos (156) \frac{1}{\cos (336)})$

Step 4.2

Convert from $\frac{1}{\cos (336)}$ to $\sec (336)$ .

$\frac{2 (\sin^{2} (150))}{1} (\cos (156) \sec (336))$

Step 5

Divide $2 (\sin^{2} (150))$ by $1$ .

$2 (\sin^{2} (150)) (\cos (156) \sec (336))$

Step 6

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

$2 \sin^{2} (30) (\cos (156) \sec (336))$

Step 7

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$2 {(\frac{1}{2})}^{2} (\cos (156) \sec (336))$

Step 8

Simplify the expression.

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Step 8.1

Apply the product rule to $\frac{1}{2}$ .

$2 \frac{1^{2}}{2^{2}} (\cos (156) \sec (336))$

Step 8.2

One to any power is one.

$2 \frac{1}{2^{2}} (\cos (156) \sec (336))$

Step 8.3

Raise $2$ to the power of $2$ .

$2 (\frac{1}{4}) (\cos (156) \sec (336))$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Factor $2$ out of $4$ .

$2 \frac{1}{2 (2)} (\cos (156) \sec (336))$

Step 9.2

Cancel the common factor.

$2 \frac{1}{2 \cdot 2} (\cos (156) \sec (336))$

Step 9.3

Rewrite the expression.

$\frac{1}{2} (\cos (156) \sec (336))$

Step 10

Multiply $\frac{1}{2} (\cos (156) \sec (336))$ .

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Step 10.1

Combine $\cos (156)$ and $\frac{1}{2}$ .

$\frac{\cos (156)}{2} \sec (336)$

Step 10.2

Combine $\frac{\cos (156)}{2}$ and $\sec (336)$ .

$\frac{\cos (156) \sec (336)}{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{\cos (156) \sec (336)}{2}$

Decimal Form:

$- 0.50000000 \dots$