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Popular >

cos(x) 1/3 e0<x<90

Solution

cos (x) \frac{1}{3} e 0 < x < 9 0^{\circ}

0 < x < 9 0^{\circ}

Interval Notation

(0, 9 0^{\circ})

Decimal Notation

0 < x < 1.57079 \dots

Solution steps

cos (x) \frac{1}{3} e 0 < x < 9 0^{\circ}

a < u < b

then

a < u and u < b

cos (x) \frac{1}{3} e 0 < x and x < 9 0^{\circ}

cos (x) \frac{1}{3} e 0 < x : x > 0

cos (x) \frac{1}{3} e 0 < x

Multiply fractions:

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

0 \cdot \frac{1 e}{3} cos (x) < x

Refine

0 < x

Move

0

to the right side

0 < x

Simplify

< x

< x

Move

x

to the left side

< x

Subtract

x

from both sides

- x < x - x

Simplify

- x < 0

- x < 0

Multiply both sides by

- 1

- x < 0

Multiply both sides by -1 (reverse the inequality)

(- x) (- 1) > 0 \cdot (- 1)

Simplify

x > 0

x > 0

Combine the intervals

x > 0 and x < 9 0^{\circ}

Merge Overlapping Intervals

x > 0 and x < 9 0^{\circ}

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

x > 0

and

x < 9 0^{\circ}

0 < x < 9 0^{\circ}

0 < x < 9 0^{\circ}

tan (θ) = 2 and cos (θ) < 0

tan (θ) = - \frac{4}{3} and sin (θ) < 0, sec (θ)

tan (x) 0 \leq x \leq \frac{π}{6}

cot (t) < 0 and sec (t) > 0

4 cos (θ) 4 sin (θ) 0 \leq θ \leq \frac{π}{2}