Trigonometry Examples

$\cos (20) x > \frac{π}{2}$

Step 1

Divide each term in $\cos (20) x > \frac{π}{2}$ by $\cos (20)$ and simplify.

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Step 1.1

Divide each term in $\cos (20) x > \frac{π}{2}$ by $\cos (20)$ .

$\frac{\cos (20) x}{\cos (20)} > \frac{\frac{π}{2}}{\cos (20)}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $\cos (20)$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{\cos (20) x}{\cos (20)} > \frac{\frac{π}{2}}{\cos (20)}$

Step 1.2.1.2

Divide $x$ by $1$ .

$x > \frac{\frac{π}{2}}{\cos (20)}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Separate fractions.

$x > \frac{\frac{π}{2}}{1} \cdot \frac{1}{\cos (20)}$

Step 1.3.2

Convert from $\frac{1}{\cos (20)}$ to $\sec (20)$ .

$x > \frac{\frac{π}{2}}{1} \sec (20)$

Step 1.3.3

Divide $\frac{π}{2}$ by $1$ .

$x > \frac{π}{2} \sec (20)$

Step 1.3.4

Evaluate $\sec (20)$ .

$x > \frac{π}{2} \cdot 2.45048752$

Step 1.3.5

Multiply $\frac{π}{2} \cdot 2.45048752$ .

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Step 1.3.5.1

Combine $\frac{π}{2}$ and $2.45048752$ .

$x > \frac{π \cdot 2.45048752}{2}$

Step 1.3.5.2

Multiply $π$ by $2.45048752$ .

$x > \frac{7.69843359}{2}$

Step 1.3.6

Divide $7.69843359$ by $2$ .

$x > 3.84921679$

Step 2

Use the inequality $x > 3.84921679$ to build the set notation.

${x | x > 3.84921679}$

Step 3