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Popular >

y= 4/(cos(x))+1/(tan(x))

Solution

y = \frac{4}{cos ( x )} + \frac{1}{tan ( x )}

Solution

Period : 2 π

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

Range : - \infty < f (x) < \infty

X Intercepts : (arcsin (2 - 5) + 2 π + 2 πn, 0), (π + arcsin (- 2 + 5) + 2 πn, 0)

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

Extreme Points : Minimum (0.59039 \dots + 2 πn, 6.30734 \dots), Maximum (π - 0.59039 \dots + 2 πn, - 6.30734 \dots)

+1

Interval Notation

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

Range : (- \infty, \infty)

Solution steps

Periodicity of

\frac{4}{cos ( x )} + \frac{1}{tan ( x )} : 2 π

Domain of

\frac{4}{cos ( x )} + \frac{1}{tan ( x )} : 2 πn < x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < π + 2 πn or π + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range of

\frac{4}{cos ( x )} + \frac{1}{tan ( x )} : - \infty < f (x) < \infty

Axis interception points of

\frac{4}{cos ( x )} + \frac{1}{tan ( x )} :

X Intercepts

: (arcsin (2 - 5) + 2 π + 2 πn, 0), (π + arcsin (- 2 + 5) + 2 πn, 0)

Asymptotes of

\frac{4}{cos ( x )} + \frac{1}{tan ( x )} :

Vertical

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

Extreme Points of

\frac{4}{cos ( x )} + \frac{1}{tan ( x )} :

Minimum

(0.59039 \dots + 2 πn, 6.30734 \dots),

Maximum

(π - 0.59039 \dots + 2 πn, - 6.30734 \dots)

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Frequently Asked Questions (FAQ)

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