English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

0<= cos(θ)<= 1

Solution

0 \leq cos (θ) \leq 1

- \frac{π}{2} + 2 πn \leq θ \leq \frac{π}{2} + 2 πn

Interval Notation

[- \frac{π}{2} + 2 πn, \frac{π}{2} + 2 πn]

Decimal Notation

- 1.57079 \dots + 2 πn \leq θ \leq 1.57079 \dots + 2 πn

Solution steps

0 \leq cos (θ) \leq 1

a \leq u \leq b

then

a \leq u and u \leq b

0 \leq cos (θ) and cos (θ) \leq 1

0 \leq cos (θ) : - \frac{π}{2} + 2 πn \leq θ \leq \frac{π}{2} + 2 πn

0 \leq cos (θ)

Switch sides

cos (θ) \geq 0

For

cos (x) \geq a

, if

- 1 < a < 1

then

- arccos (a) + 2 πn \leq x \leq arccos (a) + 2 πn

- arccos (0) + 2 πn \leq θ \leq arccos (0) + 2 πn

Simplify

- arccos (0) : - \frac{π}{2}

- arccos (0)

Use the following trivial identity:

arccos (0) = \frac{π}{2}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= - \frac{π}{2}

Simplify

arccos (0) : \frac{π}{2}

arccos (0)

Use the following trivial identity:

arccos (0) = \frac{π}{2}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{2}

- \frac{π}{2} + 2 πn \leq θ \leq \frac{π}{2} + 2 πn

cos (θ) \leq 1 :

True for all

θ \in R

cos (θ) \leq 1

Range of

cos (θ) : - 1 \leq cos (θ) \leq 1

Function range definition

The range of the basic

cos

function is

- 1 \leq cos (θ) \leq 1

- 1 \leq cos (θ) \leq 1

cos (θ) \leq 1 and - 1 \leq cos (θ) \leq 1 : - 1 \leq cos (θ) \leq 1

Let

y = cos (θ)

Combine the intervals

y \leq 1 and - 1 \leq y \leq 1

Merge Overlapping Intervals

y \leq 1 and - 1 \leq y \leq 1

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

y \leq 1

and

- 1 \leq y \leq 1

- 1 \leq y \leq 1

- 1 \leq y \leq 1

True for all θ

True for all θ \in R

Combine the intervals

- \frac{π}{2} + 2 πn \leq θ \leq \frac{π}{2} + 2 πn and True for all θ \in R

Merge Overlapping Intervals

- \frac{π}{2} + 2 πn \leq θ \leq \frac{π}{2} + 2 πn

- 2 sin^{2} (x) 0 < x < 360

- 1 \leq tan (\frac{x}{2} - \frac{π}{3}) \leq 3

- 1 \geq - cos (2 x) \geq 1

0 < 82.5 - 67.5 cos (\frac{π}{6} t) < 20

csc (x) = 4 and cot (x) < 0