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Popular >

y=sec(x/6+pi/6)

Solution

y = sec (\frac{x}{6} + \frac{π}{6})

Solution

Period : 12 π

Domain : 12 πn \leq x < 2 π + 12 πn or 2 π + 12 πn < x < 8 π + 12 πn or 8 π + 12 πn < x < 12 π + 12 πn

Range : f (x) \leq - 1 or f (x) \geq 1

Y Intercepts : (0, \frac{2 3}{3})

Asymptotes : Vertical x = 2 π + 12 πn, x = 8 π + 12 πn

Extreme Points : Maximum (5 π + 12 πn, - 1), Minimum (11 π + 12 πn, 1)

+1

Interval Notation

Domain : [12 πn, 2 π + 12 πn) \cup (2 π + 12 πn, 8 π + 12 πn) \cup (8 π + 12 πn, 12 π + 12 πn)

Range : (- \infty, - 1] \cup [1, \infty)

Solution steps

Periodicity of

sec (\frac{x}{6} + \frac{π}{6}) : 12 π

Domain of

sec (\frac{x}{6} + \frac{π}{6}) : 12 πn \leq x < 2 π + 12 πn or 2 π + 12 πn < x < 8 π + 12 πn or 8 π + 12 πn < x < 12 π + 12 πn

Range of

sec (\frac{x}{6} + \frac{π}{6}) : f (x) \leq - 1 or f (x) \geq 1

Axis interception points of

sec (\frac{x}{6} + \frac{π}{6}) :

Y Intercepts

: (0, \frac{2 3}{3})

Asymptotes of

sec (\frac{x}{6} + \frac{π}{6}) :

Vertical

: x = 2 π + 12 πn, x = 8 π + 12 πn

Extreme Points of

sec (\frac{x}{6} + \frac{π}{6}) :

Maximum

(5 π + 12 πn, - 1),

Minimum

(11 π + 12 πn, 1)

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Frequently Asked Questions (FAQ)

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