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Popular Trigonometry >

24sin(θ)>0.06>24cos(θ)

Solution

24 sin (θ) > 0.06 > 24 cos (θ)

Solution

1.56829 \dots + 2 πn < θ < π - 0.00250 \dots + 2 πn

+2

Interval Notation

(1.56829 \dots + 2 πn, π - 0.00250 \dots + 2 πn)

Decimal

1.56829 \dots + 2 πn < θ < 3.13909 \dots + 2 πn

Solution steps

24 sin (θ) > 0.06 > 24 cos (θ)

If

a > u > b

then

a > u and u > b

24 sin (θ) > 0.06 and 0.06 > 24 cos (θ)

24 sin (θ) > 0.06 : 0.00250 \dots + 2 πn < θ < π - 0.00250 \dots + 2 πn

24 sin (θ) > 0.06

Divide both sides by

24

24 sin (θ) > 0.06

Divide both sides by

24

\frac{24 sin ( θ )}{24} > \frac{0.06}{24}

Simplify

sin (θ) > 0.0025

sin (θ) > 0.0025

For

sin (x) > a

, if

- 1 \leq a < 1

then

arcsin (a) + 2 πn < x < π - arcsin (a) + 2 πn

arcsin (0.0025) + 2 πn < θ < π - arcsin (0.0025) + 2 πn

Simplify

0.00250 \dots + 2 πn < θ < π - 0.00250 \dots + 2 πn

0.06 > 24 cos (θ) : 1.56829 \dots + 2 πn < θ < 4.71488 \dots + 2 πn

0.06 > 24 cos (θ)

Switch sides

24 cos (θ) < 0.06

Divide both sides by

24

24 cos (θ) < 0.06

Divide both sides by

24

\frac{24 cos ( θ )}{24} < \frac{0.06}{24}

Simplify

cos (θ) < 0.0025

cos (θ) < 0.0025

For

cos (x) < a

, if

- 1 < a \leq 1

then

arccos (a) + 2 πn < x < 2 π - arccos (a) + 2 πn

arccos (0.0025) + 2 πn < θ < 2 π - arccos (0.0025) + 2 πn

Simplify

1.56829 \dots + 2 πn < θ < 4.71488 \dots + 2 πn

Combine the intervals

0.00250 \dots + 2 πn < θ < π - 0.00250 \dots + 2 πn and 1.56829 \dots + 2 πn < θ < 4.71488 \dots + 2 πn

Merge Overlapping Intervals

1.56829 \dots + 2 πn < θ < π - 0.00250 \dots + 2 πn

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