Trigonometry Examples

$\tan (- 45) \cos^{2} (45)$

Step 1

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 fourth quadrant.

$- \tan (45) \cos^{2} (45)$

Step 2

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

$- 1 \cdot 1 \cos^{2} (45)$

Step 3

Multiply $- 1$ by $1$ .

$- 1 \cos^{2} (45)$

Step 4

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

$- 1 {(\frac{\sqrt{2}}{2})}^{2}$

Step 5

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

$- 1 \frac{{\sqrt{2}}^{2}}{2^{2}}$

Step 6

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Step 6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- 1 \frac{{(2^{\frac{1}{2}})}^{2}}{2^{2}}$

Step 6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 1 \frac{2^{\frac{1}{2} \cdot 2}}{2^{2}}$

Step 6.3

Combine $\frac{1}{2}$ and $2$ .

$- 1 \frac{2^{\frac{2}{2}}}{2^{2}}$

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Cancel the common factor.

$- 1 \frac{2^{\frac{2}{2}}}{2^{2}}$

Step 6.4.2

Rewrite the expression.

$- 1 \frac{2^{1}}{2^{2}}$

Step 6.5

Evaluate the exponent.

$- 1 \frac{2}{2^{2}}$

Step 7

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

$- 1 (\frac{2}{4})$

Step 8

Cancel the common factor of $2$ and $4$ .

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Step 8.1

Factor $2$ out of $2$ .

$- 1 \frac{2 (1)}{4}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $4$ .

$- 1 \frac{2 \cdot 1}{2 \cdot 2}$

Step 8.2.2

Cancel the common factor.

$- 1 \frac{2 \cdot 1}{2 \cdot 2}$

Step 8.2.3

Rewrite the expression.

$- 1 (\frac{1}{2})$

Step 9

Rewrite $- 1 (\frac{1}{2})$ as $- (\frac{1}{2})$ .

$- \frac{1}{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$