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Popular >

-sin(x)<= 2/pi

Solution

- sin (x) \leq \frac{2}{π}

Solution

- arcsin (\frac{2}{π}) + 2 πn \leq x \leq π + arcsin (\frac{2}{π}) + 2 πn

+2

Interval Notation

[- arcsin (\frac{2}{π}) + 2 πn, π + arcsin (\frac{2}{π}) + 2 πn]

Decimal Notation

- 0.69010 \dots + 2 πn \leq x \leq 3.83169 \dots + 2 πn

Solution steps

- sin (x) \leq \frac{2}{π}

Multiply both sides by

- 1

- sin (x) \leq \frac{2}{π}

Multiply both sides by -1 (reverse the inequality)

(- sin (x)) (- 1) \geq \frac{2 ( - 1 )}{π}

Simplify

sin (x) \geq - \frac{2}{π}

sin (x) \geq - \frac{2}{π}

For

sin (x) \geq a

, if

- 1 < a < 1

then

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

arcsin (- \frac{2}{π}) + 2 πn \leq x \leq π - arcsin (- \frac{2}{π}) + 2 πn

Simplify

arcsin (- \frac{2}{π}) : - arcsin (\frac{2}{π})

arcsin (- \frac{2}{π})

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2}{π}) = - arcsin (\frac{2}{π})

= - arcsin (\frac{2}{π})

Simplify

π - arcsin (- \frac{2}{π}) : π + arcsin (\frac{2}{π})

π - arcsin (- \frac{2}{π})

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2}{π}) = - arcsin (\frac{2}{π})

= π - (- arcsin (\frac{2}{π}))

Apply rule

- (- a) = a

= π + arcsin (\frac{2}{π})

- arcsin (\frac{2}{π}) + 2 πn \leq x \leq π + arcsin (\frac{2}{π}) + 2 πn

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