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Popular >

f(x)=6sin(x)tan(x)+6cos(x)

Solution

f (x) = 6 sin (x) tan (x) + 6 cos (x)

Solution

Period : 2 π

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

Range : f (x) \leq - 6 or f (x) \geq 6

Y Intercepts : (0, 6)

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

Extreme Points : Minimum (2 πn, 6), Maximum (π + 2 πn, - 6)

+1

Interval Notation

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

Range : (- \infty, - 6] \cup [6, \infty)

Solution steps

Periodicity of

6 sin (x) tan (x) + 6 cos (x) : 2 π

Domain of

6 sin (x) tan (x) + 6 cos (x) : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range of

6 sin (x) tan (x) + 6 cos (x) : f (x) \leq - 6 or f (x) \geq 6

Axis interception points of

6 sin (x) tan (x) + 6 cos (x) :

Y Intercepts

: (0, 6)

Asymptotes of

6 sin (x) tan (x) + 6 cos (x) :

Vertical

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

Extreme Points of

6 sin (x) tan (x) + 6 cos (x) :

Minimum

(2 πn, 6),

Maximum

(π + 2 πn, - 6)

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