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Popular >

0.96(cos(x))(sin(x))<= 0.43

Solution

0.96 (cos (x)) (sin (x)) \leq 0.43

Solution

- \frac{π}{2} - 0.55515 \dots + πn \leq x \leq 0.55515 \dots + πn

+2

Interval Notation

[- \frac{π}{2} - 0.55515 \dots + πn, 0.55515 \dots + πn]

Decimal Notation

- 2.12594 \dots + πn \leq x \leq 0.55515 \dots + πn

Solution steps

0.96 cos (x) sin (x) \leq 0.43

Use the following identity:

2 cos (x) sin (x) = sin (2 x)

Therefore

cos (x) sin (x) = \frac{sin ( 2 x )}{2}

0.96 \cdot \frac{sin ( 2 x )}{2} \leq 0.43

Simplify

0.96 \cdot \frac{sin ( 2 x )}{2} : \frac{0.96}{2} sin (2 x)

0.96 \cdot \frac{sin ( 2 x )}{2}

Multiply fractions:

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

= \frac{sin ( 2 x ) \cdot 0.96}{2}

= \frac{0.96}{2} sin (2 x)

\frac{0.96}{2} sin (2 x) \leq 0.43

Multiply both sides by

2

\frac{0.96}{2} sin (2 x) \leq 0.43

Multiply both sides by

2

2 \cdot \frac{0.96}{2} sin (2 x) \leq 0.43 \cdot 2

Simplify

0.96 sin (2 x) \leq 0.86

0.96 sin (2 x) \leq 0.86

Divide both sides by

0.96

0.96 sin (2 x) \leq 0.86

Divide both sides by

0.96

\frac{0.96 sin ( 2 x )}{0.96} \leq \frac{0.86}{0.96}

Simplify

sin (2 x) \leq 0.89583 \dots

sin (2 x) \leq 0.89583 \dots

For

sin (x) \leq a

, if

- 1 < a < 1

then

- π - arcsin (a) + 2 πn \leq x \leq arcsin (a) + 2 πn

- π - arcsin (0.89583 \dots) + 2 πn \leq 2 x \leq arcsin (0.89583 \dots) + 2 πn

If

a \leq u \leq b

then

a \leq u and u \leq b

- π - arcsin (0.89583 \dots) + 2 πn \leq 2 x and 2 x \leq arcsin (0.89583 \dots) + 2 πn

- π - arcsin (0.89583 \dots) + 2 πn \leq 2 x : x \geq - \frac{π}{2} - 0.55515 \dots + πn

- π - arcsin (0.89583 \dots) + 2 πn \leq 2 x

Switch sides

2 x \geq - π - arcsin (0.89583 \dots) + 2 πn

Divide both sides by

2

2 x \geq - π - arcsin (0.89583 \dots) + 2 πn

Divide both sides by

2

\frac{2 x}{2} \geq - \frac{π}{2} - \frac{arcsin ( 0.89583 \dots )}{2} + \frac{2 πn}{2}

Simplify

\frac{2 x}{2} \geq - \frac{π}{2} - \frac{arcsin ( 0.89583 \dots )}{2} + \frac{2 πn}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

- \frac{π}{2} - \frac{arcsin ( 0.89583 \dots )}{2} + \frac{2 πn}{2} : - \frac{π}{2} - 0.55515 \dots + πn

- \frac{π}{2} - \frac{arcsin ( 0.89583 \dots )}{2} + \frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= - \frac{π}{2} - \frac{arcsin ( 0.89583 \dots )}{2} + πn

\frac{arcsin ( 0.89583 \dots )}{2} = 0.55515 \dots

\frac{arcsin ( 0.89583 \dots )}{2}

arcsin (0.89583 \dots) = 1.11030 \dots

= \frac{1.11030 \dots}{2}

Divide the numbers:

\frac{1.11030 \dots}{2} = 0.55515 \dots

= 0.55515 \dots

= - \frac{π}{2} - 0.55515 \dots + πn

x \geq - \frac{π}{2} - 0.55515 \dots + πn

x \geq - \frac{π}{2} - 0.55515 \dots + πn

x \geq - \frac{π}{2} - 0.55515 \dots + πn

2 x \leq arcsin (0.89583 \dots) + 2 πn : x \leq 0.55515 \dots + πn

2 x \leq arcsin (0.89583 \dots) + 2 πn

Divide both sides by

2

2 x \leq arcsin (0.89583 \dots) + 2 πn

Divide both sides by

2

\frac{2 x}{2} \leq \frac{arcsin ( 0.89583 \dots )}{2} + \frac{2 πn}{2}

Simplify

\frac{2 x}{2} \leq \frac{arcsin ( 0.89583 \dots )}{2} + \frac{2 πn}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{arcsin ( 0.89583 \dots )}{2} + \frac{2 πn}{2} : 0.55515 \dots + πn

\frac{arcsin ( 0.89583 \dots )}{2} + \frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{arcsin ( 0.89583 \dots )}{2} + πn

\frac{arcsin ( 0.89583 \dots )}{2} = 0.55515 \dots

\frac{arcsin ( 0.89583 \dots )}{2}

arcsin (0.89583 \dots) = 1.11030 \dots

= \frac{1.11030 \dots}{2}

Divide the numbers:

\frac{1.11030 \dots}{2} = 0.55515 \dots

= 0.55515 \dots

= 0.55515 \dots + πn

x \leq 0.55515 \dots + πn

x \leq 0.55515 \dots + πn

x \leq 0.55515 \dots + πn

Combine the intervals

x \geq - \frac{π}{2} - 0.55515 \dots + πn and x \leq 0.55515 \dots + πn

Merge Overlapping Intervals

- \frac{π}{2} - 0.55515 \dots + πn \leq x \leq 0.55515 \dots + πn

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