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Popular Trigonometry >

cos^2(x)>14

Solution

cos^{2} (x) > 14

Solution

No Solution for x \in R

Solution steps

cos^{2} (x) > 14

For

u^{n} > a

, if

n

is even then

cos (x) < - 14 or cos (x) > 14

cos (x) < - 14 :

False for all

x \in R

cos (x) < - 14

Range of

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

Function range definition

The range of the basic

cos

function is

- 1 \leq cos (x) \leq 1

- 1 \leq cos (x) \leq 1

cos (x) < - 14 and - 1 \leq cos (x) \leq 1 :

False

Let

y = cos (x)

Combine the intervals

y < - 14 and - 1 \leq y \leq 1

Merge Overlapping Intervals

y < - 14 and - 1 \leq y \leq 1

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

y < - 14

and

- 1 \leq y \leq 1

False for all y \in R

False for all y \in R

No Solution for x \in R

False for all x \in R

cos (x) > 14 :

False for all

x \in R

cos (x) > 14

Range of

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

Function range definition

The range of the basic

cos

function is

- 1 \leq cos (x) \leq 1

- 1 \leq cos (x) \leq 1

cos (x) > 14 and - 1 \leq cos (x) \leq 1 :

False

Let

y = cos (x)

Combine the intervals

y > 14 and - 1 \leq y \leq 1

Merge Overlapping Intervals

y > 14 and - 1 \leq y \leq 1

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

y > 14

and

- 1 \leq y \leq 1

False for all y \in R

False for all y \in R

No Solution for x \in R

False for all x \in R

Combine the intervals

False for all x \in R or False for all x \in R

Merge Overlapping Intervals

False for all x \in R or False for all x \in R

The union of two intervals is the set of numbers which are in either interval

False for all

x \in R

False for all

x \in R

False for all x \in R

No Solution for x \in R

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