Trigonometry Examples

$\tan (- \frac{7}{15}) \sec (x) > 0$

Step 1

Divide each term in $\tan (- \frac{7}{15}) \sec (x) > 0$ by $\tan (- \frac{7}{15})$ and simplify.

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Step 1.1

Divide each term in $\tan (- \frac{7}{15}) \sec (x) > 0$ by $\tan (- \frac{7}{15})$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{\tan (- \frac{7}{15}) \sec (x)}{\tan (- \frac{7}{15})} < \frac{0}{\tan (- \frac{7}{15})}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $\tan (- \frac{7}{15})$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{\tan (- \frac{7}{15}) \sec (x)}{\tan (- \frac{7}{15})} < \frac{0}{\tan (- \frac{7}{15})}$

Step 1.2.1.2

Divide $\sec (x)$ by $1$ .

$\sec (x) < \frac{0}{\tan (- \frac{7}{15})}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Separate fractions.

$\sec (x) < \frac{0}{1} \cdot \frac{1}{\tan (- \frac{7}{15})}$

Step 1.3.2

Rewrite $\tan (- \frac{7}{15})$ in terms of sines and cosines.

$\sec (x) < \frac{0}{1} \cdot \frac{1}{\frac{\sin (- \frac{7}{15})}{\cos (- \frac{7}{15})}}$

Step 1.3.3

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (- \frac{7}{15})}{\cos (- \frac{7}{15})}$ .

$\sec (x) < \frac{0}{1} \cdot \frac{\cos (- \frac{7}{15})}{\sin (- \frac{7}{15})}$

Step 1.3.4

Convert from $\frac{\cos (- \frac{7}{15})}{\sin (- \frac{7}{15})}$ to $\cot (- \frac{7}{15})$ .

$\sec (x) < \frac{0}{1} \cot (- \frac{7}{15})$

Step 1.3.5

Divide $0$ by $1$ .

$\sec (x) < 0 \cot (- \frac{7}{15})$

Step 1.3.6

Evaluate $\cot (- \frac{7}{15})$ .

$\sec (x) < 0 \cdot - 1.98499526$

Step 1.3.7

Multiply $0$ by $- 1.98499526$ .

$\sec (x) < 0$

Step 2

The range of secant is $y \leq - 1$ and $y \geq 1$ . Since $0$ does not fall in this range, there is no solution.

No solution