Algebra Examples

$E = \sin^{2} (30 °) + \tan (37 °)$

Step 1

Simplify each term.

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Step 1.1

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

$E = {(\frac{1}{2})}^{2} + \tan (37 °)$

Step 1.2

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

$E = \frac{1^{2}}{2^{2}} + \tan (37 °)$

Step 1.3

One to any power is one.

$E = \frac{1}{2^{2}} + \tan (37 °)$

Step 1.4

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

$E = \frac{1}{4} + \tan (37 °)$

Step 1.5

Evaluate $\tan (37 °)$ .

$E = \frac{1}{4} + 0.75355405$

Step 2

To write $0.75355405$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$E = \frac{1}{4} + 0.75355405 \cdot \frac{4}{4}$

Step 3

Combine fractions.

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Step 3.1

Combine $0.75355405$ and $\frac{4}{4}$ .

$E = \frac{1}{4} + \frac{0.75355405 \cdot 4}{4}$

Step 3.2

Combine the numerators over the common denominator.

$E = \frac{1 + 0.75355405 \cdot 4}{4}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $0.75355405$ by $4$ .

$E = \frac{1 + 3.0142162}{4}$

Step 4.2

Add $1$ and $3.0142162$ .

$E = \frac{4.0142162}{4}$

Step 5

Divide $4.0142162$ by $4$ .

$E = 1.00355405$