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Popular >

(11pi)/9 <= arctan(θ)<= (13pi)/9

Solution

\frac{11 π}{9} \leq arctan (θ) \leq \frac{13 π}{9}

Solution

False for all θ \in R

Solution steps

\frac{11 π}{9} \leq arctan (θ) \leq \frac{13 π}{9}

a \leq u \leq b

then

a \leq u and u \leq b

\frac{11 π}{9} \leq arctan (θ) and arctan (θ) \leq \frac{13 π}{9}

\frac{11 π}{9} \leq arctan (θ) :

False for all

θ \in R

\frac{11 π}{9} \leq arctan (θ)

Switch sides

arctan (θ) \geq \frac{11 π}{9}

Range of

arctan (θ) : - \frac{π}{2} < arctan (θ) < \frac{π}{2}

Function range definition

The range of the basic

arctan

function is

- \frac{π}{2} < arctan (θ) < \frac{π}{2}

- \frac{π}{2} < arctan (θ) < \frac{π}{2}

arctan (θ) \geq \frac{11 π}{9} and - \frac{π}{2} < arctan (θ) < \frac{π}{2} :

False

Let

y = arctan (θ)

Combine the intervals

y \geq \frac{11 π}{9} and - \frac{π}{2} < y < \frac{π}{2}

Merge Overlapping Intervals

y \geq \frac{11 π}{9} and - \frac{π}{2} < y < \frac{π}{2}

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

y \geq \frac{11 π}{9}

and

- \frac{π}{2} < y < \frac{π}{2}

False for all y \in R

False for all y \in R

No Solution for θ \in R

False for all θ \in R

arctan (θ) \leq \frac{13 π}{9} :

True for all

θ \in R

arctan (θ) \leq \frac{13 π}{9}

Range of

arctan (θ) : - \frac{π}{2} < arctan (θ) < \frac{π}{2}

Function range definition

The range of the basic

arctan

function is

- \frac{π}{2} < arctan (θ) < \frac{π}{2}

- \frac{π}{2} < arctan (θ) < \frac{π}{2}

arctan (θ) \leq \frac{13 π}{9} and - \frac{π}{2} < arctan (θ) < \frac{π}{2} : - \frac{π}{2} < arctan (θ) < \frac{π}{2}

Let

y = arctan (θ)

Combine the intervals

y \leq \frac{13 π}{9} and - \frac{π}{2} < y < \frac{π}{2}

Merge Overlapping Intervals

y \leq \frac{13 π}{9} 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 \frac{13 π}{9}

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 θ

True for all θ \in R

Combine the intervals

False for all θ \in R and True for all θ \in R

Merge Overlapping Intervals

False for all θ \in R and True for all θ \in R

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

False for all

θ \in R

and

True for all

θ \in R

False for all θ \in R

False for all θ \in R

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