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Popular >

y=(sin(x)+cos(x))/(tan(x))

Solution

y = \frac{sin ( x ) + cos ( x )}{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

X Intercepts : (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0)

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

+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)

Solution steps

Periodicity of

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

Domain of

\frac{sin ( x ) + cos ( x )}{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

Axis interception points of

\frac{sin ( x ) + cos ( x )}{tan ( x )} :

X Intercepts

: (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0)

Asymptotes of

\frac{sin ( x ) + cos ( x )}{tan ( x )} :

Vertical

: x = 2 πn, x = π + 2 πn

Popular Examples

h (x) = x^{2} - 2 x - 3

y = - 10 x + 8

f(x)=sqrt(x^4-81)

f (x) = x^{4} - 81

f (x) = \frac{x ^{2} + 5}{x}

y = - 8 x + 8

Frequently Asked Questions (FAQ)

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