Find the Exact Value sec(42 degrees 12')

$\sec (\frac{211}{5})$

Step 1

Since $42$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $12$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $0$ by $\frac{1}{3600}$ . Add them together.

$\sec (42 + 12 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600})$

Step 2

Simplify.

Remove parentheses.

$\sec (42 + 12 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600})$

Simplify each term.

Cancel the common factor of $12$ .

Factor $12$ out of $60$ .

$\sec (42 + 12 \cdot \frac{1}{12 (5)} + 0 \cdot \frac{1}{3600})$

Cancel the common factor.

$\sec (42 + 12 \cdot \frac{1}{12 \cdot 5} + 0 \cdot \frac{1}{3600})$

Rewrite the expression.

$\sec (42 + \frac{1}{5} + 0 \cdot \frac{1}{3600})$

Multiply $0$ by $\frac{1}{3600}$ .

$\sec (42 + \frac{1}{5} + 0)$

To write $42$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\sec (42 \cdot \frac{5}{5} + \frac{1}{5} + 0)$

Combine $42$ and $\frac{5}{5}$ .

$\sec (\frac{42 \cdot 5}{5} + \frac{1}{5} + 0)$

Combine the numerators over the common denominator.

$\sec (\frac{42 \cdot 5 + 1}{5} + 0)$

Simplify the numerator.

Multiply $42$ by $5$ .

$\sec (\frac{210 + 1}{5} + 0)$

Add $210$ and $1$ .

$\sec (\frac{211}{5} + 0)$

Add $\frac{211}{5}$ and $0$ .

$\sec (\frac{211}{5})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sec (\frac{211}{5})$

Decimal Form:

$1.34988363 \dots$

Find the Exact Value sec(42 degrees 12')

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