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Popular >

|sin(x)|= 2/pi

Solution

∣ sin (x) ∣ = \frac{2}{π}

Solution

x = - 0.69010 \dots + 2 πn, x = π + 0.69010 \dots + 2 πn, x = 0.69010 \dots + 2 πn, x = π - 0.69010 \dots + 2 πn

+1

Degrees

x = - 39.54022 \dots^{\circ} + 36 0^{\circ} n, x = 219.54022 \dots^{\circ} + 36 0^{\circ} n, x = 39.54022 \dots^{\circ} + 36 0^{\circ} n, x = 140.45977 \dots^{\circ} + 36 0^{\circ} n

Solution steps

∣ sin (x) ∣ = \frac{2}{π}

Solve by substitution

∣ sin (x) ∣ = \frac{2}{π}

Let:

sin (x) = u

∣ u ∣ = \frac{2}{π}

∣ u ∣ = \frac{2}{π} : u = - \frac{2}{π} or u = \frac{2}{π}

∣ u ∣ = \frac{2}{π}

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

or

u = - a

u = - \frac{2}{π} or u = \frac{2}{π}

Substitute back

u = sin (x)

sin (x) = - \frac{2}{π} or sin (x) = \frac{2}{π}

sin (x) = - \frac{2}{π} or sin (x) = \frac{2}{π}

sin (x) = - \frac{2}{π} : x = arcsin (- \frac{2}{π}) + 2 πn, x = π + arcsin (\frac{2}{π}) + 2 πn

sin (x) = - \frac{2}{π}

Apply trig inverse properties

sin (x) = - \frac{2}{π}

General solutions for

sin (x) = - \frac{2}{π}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

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

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

sin (x) = \frac{2}{π} : x = arcsin (\frac{2}{π}) + 2 πn, x = π - arcsin (\frac{2}{π}) + 2 πn

sin (x) = \frac{2}{π}

Apply trig inverse properties

sin (x) = \frac{2}{π}

General solutions for

sin (x) = \frac{2}{π}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

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

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

Combine all the solutions

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

Show solutions in decimal form

x = - 0.69010 \dots + 2 πn, x = π + 0.69010 \dots + 2 πn, x = 0.69010 \dots + 2 πn, x = π - 0.69010 \dots + 2 πn

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