English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2-sin^2(x)>= 0

Solution

2 - sin^{2} (x) \geq 0

Solution

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

2 - sin^{2} (x) \geq 0

Move

2

to the right side

2 - sin^{2} (x) \geq 0

Subtract

2

from both sides

2 - sin^{2} (x) - 2 \geq 0 - 2

Simplify

- sin^{2} (x) \geq - 2

- sin^{2} (x) \geq - 2

Multiply both sides by

- 1

- sin^{2} (x) \geq - 2

Multiply both sides by -1 (reverse the inequality)

(- sin^{2} (x)) (- 1) \leq (- 2) (- 1)

Simplify

sin^{2} (x) \leq 2

sin^{2} (x) \leq 2

For

u^{n} \leq a

, if

n

is even then

- 2 \leq sin (x) \leq 2

a \leq u \leq b

then

a \leq u and u \leq b

- 2 \leq sin (x) and sin (x) \leq 2

- 2 \leq sin (x) :

True for all

x \in R

- 2 \leq sin (x)

Switch sides

sin (x) \geq - 2

Range of

sin (x) : - 1 \leq sin (x) \leq 1

Function range definition

The range of the basic

sin

function is

- 1 \leq sin (x) \leq 1

- 1 \leq sin (x) \leq 1

sin (x) \geq - 2 and - 1 \leq sin (x) \leq 1 : - 1 \leq sin (x) \leq 1

Let

y = sin (x)

Combine the intervals

y \geq - 2 and - 1 \leq y \leq 1

Merge Overlapping Intervals

y \geq - 2 and - 1 \leq y \leq 1

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

y \geq - 2

and

- 1 \leq y \leq 1

- 1 \leq y \leq 1

- 1 \leq y \leq 1

True for all x

True for all x \in R

sin (x) \leq 2 :

True for all

x \in R

sin (x) \leq 2

Range of

sin (x) : - 1 \leq sin (x) \leq 1

Function range definition

The range of the basic

sin

function is

- 1 \leq sin (x) \leq 1

- 1 \leq sin (x) \leq 1

sin (x) \leq 2 and - 1 \leq sin (x) \leq 1 : - 1 \leq sin (x) \leq 1

Let

y = sin (x)

Combine the intervals

y \leq 2 and - 1 \leq y \leq 1

Merge Overlapping Intervals

y \leq 2 and - 1 \leq y \leq 1

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

y \leq 2

and

- 1 \leq y \leq 1

- 1 \leq y \leq 1

- 1 \leq y \leq 1

True for all x

True for all x \in R

Combine the intervals

True for all x \in R and True for all x \in R

Merge Overlapping Intervals

True for all x \in R and True for all x \in R

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

True for all

x \in R

and

True for all

x \in R

True for all x \in R

True for all x

Popular Examples

cos(θ)<0,tan(θ)>0

cos (θ) < 0, tan (θ) > 0

3cos^2(x)+5cos(x)-2<0

3 cos^{2} (x) + 5 cos (x) - 2 < 0

cos(x)<= 1/2

cos (x) \leq \frac{1}{2}

1+cos(2t)>= 0

1 + cos (2 t) \geq 0

15cos(pi/(15)x-(2pi)/3)+95<= 105

15 cos (\frac{π}{15} x - \frac{2 π}{3}) + 95 \leq 105