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Popular >

0<= arctan(x)<= 1

Solution

0 \leq arctan (x) \leq 1

Solution

0 \leq x \leq tan (1)

+2

Interval Notation

[0, tan (1)]

Decimal Notation

0 \leq x \leq 1.55740 \dots

Solution steps

0 \leq arctan (x) \leq 1

If

a \leq u \leq b

then

a \leq u and u \leq b

0 \leq arctan (x) and arctan (x) \leq 1

0 \leq arctan (x) : x \geq 0

0 \leq arctan (x)

Switch sides

arctan (x) \geq 0

If

arctan (x) \geq a

then

x \geq tan (a)

x \geq tan (0)

tan (0) = 0

tan (0)

Use the following trivial identity:

tan (0) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

x \geq 0

arctan (x) \leq 1 : x \leq tan (1)

arctan (x) \leq 1

If

arctan (x) \leq a

then

x \leq tan (a)

x \leq tan (1)

Combine the intervals

x \geq 0 and x \leq tan (1)

Merge Overlapping Intervals

x \geq 0 and x \leq tan (1)

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

x \geq 0

and

x \leq tan (1)

0 \leq x \leq tan (1)

0 \leq x \leq tan (1)

Popular Examples

tan(θ)>0\land sin(θ)<0

tan (θ) > 0 and sin (θ) < 0

sin(θ)<0\land cos(θ)>0

sin (θ) < 0 and cos (θ) > 0

cot(θ)=-1/3 \land cos(θ)>0,sec(θ)

cot (θ) = - \frac{1}{3} and cos (θ) > 0, sec (θ)

tan(θ)=-4/5 \land cos(θ)>0,csc(θ)

tan (θ) = - \frac{4}{5} and cos (θ) > 0, csc (θ)

-1/2 <cos(x)< 1/2

- \frac{1}{2} < cos (x) < \frac{1}{2}