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Popular >

f(x)=arcsin(sqrt(2)sin(x))

Solution

f (x) = arcsin (2 sin (x))

Solution

Domain : 2 πn \leq x \leq \frac{π}{4} + 2 πn or \frac{3 π}{4} + 2 πn \leq x \leq \frac{5 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn \leq x < 2 π + 2 πn

Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Minimum (0, 0), Maximum (\frac{π}{4}, \frac{π}{2}), Maximum (\frac{3 π}{4}, \frac{π}{2}), Minimum (\frac{5 π}{4}, - \frac{π}{2}), Minimum (\frac{7 π}{4}, - \frac{π}{2})

+1

Interval Notation

Domain : [2 πn, \frac{π}{4} + 2 πn] \cup [\frac{3 π}{4} + 2 πn, \frac{5 π}{4} + 2 πn] \cup [\frac{7 π}{4} + 2 πn, 2 π + 2 πn)

Solution steps

Domain of

arcsin (2 sin (x)) : 2 πn \leq x \leq \frac{π}{4} + 2 πn or \frac{3 π}{4} + 2 πn \leq x \leq \frac{5 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn \leq x < 2 π + 2 πn

Axis interception points of

arcsin (2 sin (x)) :

Y Intercepts

: (0, 0)

Asymptotes of

arcsin (2 sin (x)) :

None

Extreme Points of

arcsin (2 sin (x)) :

Minimum

(0, 0),

Maximum

(\frac{π}{4}, \frac{π}{2}),

Maximum

(\frac{3 π}{4}, \frac{π}{2}),

Minimum

(\frac{5 π}{4}, - \frac{π}{2}),

Minimum

(\frac{7 π}{4}, - \frac{π}{2})

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Frequently Asked Questions (FAQ)

What is the f(x)=arcsin(sqrt(2)sin(x)) ?
The f(x)=arcsin(sqrt(2)sin(x)) is