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Popular >

arctan(x)-pi/2 <0.1

Solution

arctan (x) - \frac{π}{2} < 0.1

Solution

True for all x \in R

+1

Interval Notation

(- \infty, \infty)

Solution steps

arctan (x) - \frac{π}{2} < 0.1

Move

\frac{π}{2}

to the right side

arctan (x) - \frac{π}{2} < 0.1

Add

\frac{π}{2}

to both sides

arctan (x) - \frac{π}{2} + \frac{π}{2} < 0.1 + \frac{π}{2}

Simplify

arctan (x) < 0.1 + \frac{π}{2}

arctan (x) < 0.1 + \frac{π}{2}

Range of

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

Function range definition

The range of the basic

arctan

function is

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

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

arctan (x) < 0.1 + \frac{π}{2} and - \frac{π}{2} < arctan (x) < \frac{π}{2} : - \frac{π}{2} < arctan (x) < \frac{π}{2}

Let

y = arctan (x)

Combine the intervals

y < 0.1 + \frac{π}{2} and - \frac{π}{2} < y < \frac{π}{2}

Merge Overlapping Intervals

y < 0.1 + \frac{π}{2} and - \frac{π}{2} < y < \frac{π}{2}

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

y < 0.1 + \frac{π}{2}

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 x

True for all x \in R

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