English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

90-arctan((0.5*3x)/2)>= 40

Solution

90 - arctan (\frac{0.5 \cdot 3 x}{2}) \geq 40

True for all x \in R

Interval Notation

(- \infty, \infty)

Solution steps

90 - arctan (\frac{0.5 \cdot 3 x}{2}) \geq 40

Move

90

to the right side

90 - arctan (\frac{0.5 \cdot 3 x}{2}) \geq 40

Subtract

90

from both sides

90 - arctan (\frac{0.5 \cdot 3 x}{2}) - 90 \geq 40 - 90

Simplify

- arctan (\frac{0.5 \cdot 3 x}{2}) \geq - 50

- arctan (\frac{0.5 \cdot 3 x}{2}) \geq - 50

Multiply both sides by

- 1

- arctan (\frac{0.5 \cdot 3 x}{2}) \geq - 50

Multiply both sides by -1 (reverse the inequality)

(- arctan (\frac{0.5 \cdot 3 x}{2})) (- 1) \leq (- 50) (- 1)

Simplify

arctan (\frac{0.5 \cdot 3 x}{2}) \leq 50

arctan (\frac{0.5 \cdot 3 x}{2}) \leq 50

Range of

arctan (\frac{0.5 \cdot 3 x}{2}) : - \frac{π}{2} < arctan (\frac{0.5 \cdot 3 x}{2}) < \frac{π}{2}

Function range definition

The range of the basic

arctan

function is

- \frac{π}{2} < arctan (\frac{0.5 \cdot 3 x}{2}) < \frac{π}{2}

- \frac{π}{2} < arctan (\frac{0.5 \cdot 3 x}{2}) < \frac{π}{2}

arctan (\frac{0.5 \cdot 3 x}{2}) \leq 50 and - \frac{π}{2} < arctan (\frac{0.5 \cdot 3 x}{2}) < \frac{π}{2} : - \frac{π}{2} < arctan (\frac{0.5 \cdot 3 x}{2}) < \frac{π}{2}

Let

y = arctan (\frac{0.5 \cdot 3 x}{2})

Combine the intervals

y \leq 50 and - \frac{π}{2} < y < \frac{π}{2}

Merge Overlapping Intervals

y \leq 50 and - \frac{π}{2} < y < \frac{π}{2}

The intersection of two intervals is the set of numbers which are in both intervals

y \leq 50

and

- \frac{π}{2} < y < \frac{π}{2}

- \frac{π}{2} < y < \frac{π}{2}

- \frac{π}{2} < y < \frac{π}{2}

True for all x

True for all x \in R

- sin (x) \leq \frac{2}{π}

sin (x) > - 1, 0 \leq x \leq 2 π

tan (θ) > 0, cos (θ) < 0 sin (θ) = - \frac{2}{5}, tan (θ) = θ

cos (θ) \geq - \frac{1}{2}

x, arctan (x) < 0.0001