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Popular >

tan^2(x)>sqrt(5),-pi<= x<= pi

Solution

tan^{2} (x) > 5, - π \leq x \leq π

Solution

+2

Interval Notation

Decimal Notation

0.98135 \dots + πn < x < 1.57079 \dots + πn or - 1.57079 \dots + πn < x < - 0.98135 \dots + πn

Solution steps

tan^{2} (x) > 5, - π \leq x \leq π

For

u^{n} > a

, if

n

is even then

tan (x) < - 5 or tan (x) > 5

5

Apply radical rule:

a = a^{\frac{1}{2}}

= (5^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 5^{\frac{1}{2} \cdot \frac{1}{2}}

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

\frac{1}{2} \cdot \frac{1}{2}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 \cdot 2}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

= 5^{\frac{1}{4}}

If

tan (x) < a

then

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

Simplify

Use the following property:

arctan (- x) = - arctan (x)

If

tan (x) > a

then

arctan (a) + πn < x < \frac{π}{2} + πn

Combine the intervals

Merge Overlapping Intervals

Popular Examples

tan (x) \leq - 1

sin (x) < 0.5

sin(x)>(sqrt(2))/2

sin (x) > \frac{2}{2}

4sin^2(x)-2(1+sqrt(2))sin(x)+sqrt(2)<0

4 sin^{2} (x) - 2 (1 + 2) sin (x) + 2 < 0

cos((pit)/2) pi/2 >0

cos (\frac{π t}{2}) \frac{π}{2} > 0