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Popular >

(10pi)/9 <= arctan(θ)

Solution

\frac{10 π}{9} \leq arctan (θ)

Solution

False for all θ \in R

Solution steps

\frac{10 π}{9} \leq arctan (θ)

Switch sides

arctan (θ) \geq \frac{10 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{10 π}{9} and - \frac{π}{2} < arctan (θ) < \frac{π}{2} :

False

Let

y = arctan (θ)

Combine the intervals

y \geq \frac{10 π}{9} and - \frac{π}{2} < y < \frac{π}{2}

Merge Overlapping Intervals

y \geq \frac{10 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{10 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

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arctan(x/6)<= 0.003

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tan (9 0^{\circ} - θ) > 1