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Popular >

0<= sin^2(x)<= 1

Solution

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

Solution

True for all x \in R

Interval Notation

(- \infty, \infty)

Solution steps

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

a \leq u \leq b

then

a \leq u and u \leq b

0 \leq sin^{2} (x) and sin^{2} (x) \leq 1

0 \leq sin^{2} (x) :

True for all

x

0 \leq sin^{2} (x)

Switch sides

sin^{2} (x) \geq 0

If n is even,

u^{n} \geq 0

for all

u

True for all x

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

True for all

x

sin^{2} (x) \leq 1

For

u^{n} \leq a

, if

n

is even then

- 1 \leq sin (x) \leq 1

a \leq u \leq b

then

a \leq u and u \leq b

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

- 1 \leq sin (x) :

True for all

x \in R

- 1 \leq sin (x)

Switch sides

sin (x) \geq - 1

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

Let

y = sin (x)

Combine the intervals

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

Merge Overlapping Intervals

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

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

y \geq - 1

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 1 :

True for all

x \in R

sin (x) \leq 1

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

Let

y = sin (x)

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 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

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 \in R

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