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Popular >

f(x)=tan(x)-cos(x)

Solution

f (x) = tan (x) - 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 : - \infty < f (x) < \infty

X Intercepts : (arcsin (\frac{- 1 + 5}{2}) + 2 πn, 0), (π - arcsin (\frac{- 1 + 5}{2}) + 2 πn, 0), Y Intercepts : (0, - 1)

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

Extreme Points : None

+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, \infty)

Solution steps

Periodicity of

tan (x) - cos (x) : 2 π

Domain of

tan (x) - 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

tan (x) - cos (x) : - \infty < f (x) < \infty

Axis interception points of

tan (x) - cos (x) :

X Intercepts

: (arcsin (\frac{- 1 + 5}{2}) + 2 πn, 0), (π - arcsin (\frac{- 1 + 5}{2}) + 2 πn, 0),

Y Intercepts

: (0, - 1)

Asymptotes of

tan (x) - cos (x) :

Vertical

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

Extreme Points of

tan (x) - cos (x) :

None

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Frequently Asked Questions (FAQ)

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