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Popular >

y=2csc(x-pi/3)

Solution

y = 2 csc (x - \frac{π}{3})

Solution

Period : 2 π

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

Range : f (x) \leq - 2 or f (x) \geq 2

Y Intercepts : (0, - \frac{4 3}{3})

Asymptotes : Vertical x = \frac{π}{3} + 2 πn, x = π + \frac{π}{3} + 2 πn

Extreme Points : Minimum (\frac{5 π}{6} + 2 πn, 2), Maximum (\frac{11 π}{6} + 2 πn, - 2)

+1

Interval Notation

Domain : [2 πn, \frac{π}{3} + 2 πn) \cup (\frac{π}{3} + 2 πn, π + \frac{π}{3} + 2 πn) \cup (π + \frac{π}{3} + 2 πn, 2 π + 2 πn)

Range : (- \infty, - 2] \cup [2, \infty)

Solution steps

Periodicity of

2 csc (x - \frac{π}{3}) : 2 π

Domain of

2 csc (x - \frac{π}{3}) : 2 πn \leq x < \frac{π}{3} + 2 πn or \frac{π}{3} + 2 πn < x < π + \frac{π}{3} + 2 πn or π + \frac{π}{3} + 2 πn < x < 2 π + 2 πn

Range of

2 csc (x - \frac{π}{3}) : f (x) \leq - 2 or f (x) \geq 2

Axis interception points of

2 csc (x - \frac{π}{3}) :

Y Intercepts

: (0, - \frac{4 3}{3})

Asymptotes of

2 csc (x - \frac{π}{3}) :

Vertical

: x = \frac{π}{3} + 2 πn, x = π + \frac{π}{3} + 2 πn

Extreme Points of

2 csc (x - \frac{π}{3}) :

Minimum

(\frac{5 π}{6} + 2 πn, 2),

Maximum

(\frac{11 π}{6} + 2 πn, - 2)

Popular Examples

y=sin(sin(sin(x)))

y = sin (sin (sin (x)))

f(x)=x^4+2x^3+3x^2+2x+2

f (x) = x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 2

f(x)=x+sqrt(x^2-1)

f (x) = x + x^{2} - 1

intercepts of-x,x<0 intercepts

- x, x < 0

extreme f(y_{=3x^2-8x+5})=y_{=3x^2-8x+5}(x)extreme points

f (y_{= 3 x^{2} - 8 x + 5}) = y_{= 3 x^{2} - 8 x + 5} (x)

Frequently Asked Questions (FAQ)

What is the y=2csc(x-pi/3) ?
The y=2csc(x-pi/3) is