Trigonometry Examples

$r = - 1^{2} - {(\sqrt{3})}^{2}$

Step 1

Remove parentheses.

$r = - 1^{2} - {\sqrt{3}}^{2}$

Step 2

Simplify $- 1^{2} - {\sqrt{3}}^{2}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

One to any power is one.

$r = - 1 \cdot 1 - {\sqrt{3}}^{2}$

Step 2.1.2

Multiply $- 1$ by $1$ .

$r = - 1 - {\sqrt{3}}^{2}$

Step 2.1.3

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 2.1.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$r = - 1 - {(3^{\frac{1}{2}})}^{2}$

Step 2.1.3.2

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

$r = - 1 - 3^{\frac{1}{2} \cdot 2}$

Step 2.1.3.3

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

$r = - 1 - 3^{\frac{2}{2}}$

Step 2.1.3.4

Cancel the common factor of $2$ .

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Step 2.1.3.4.1

Cancel the common factor.

$r = - 1 - 3^{\frac{2}{2}}$

Step 2.1.3.4.2

Rewrite the expression.

$r = - 1 - 3^{1}$

Step 2.1.3.5

Evaluate the exponent.

$r = - 1 - 1 \cdot 3$

Step 2.1.4

Multiply $- 1$ by $3$ .

$r = - 1 - 3$

Step 2.2

Subtract $3$ from $- 1$ .

$r = - 4$