en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

f(θ)=sec(θ)-1

Solution

f (θ) = sec (θ) - 1

Solution

Period : 2 π

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

Range : f (θ) \leq - 2 or f (θ) \geq 0

X Intercepts : (2 πn, 0), Y Intercepts : (0, 0)

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

Extreme Points : Minimum (2 πn, 0), Maximum (π + 2 πn, - 2)

+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, - 2] \cup [0, \infty)

Solution steps

Periodicity of

sec (θ) - 1 : 2 π

Domain of

sec (θ) - 1 : 2 πn \leq θ < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < θ < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < θ < 2 π + 2 πn

Range of

sec (θ) - 1 : f (θ) \leq - 2 or f (θ) \geq 0

Axis interception points of

sec (θ) - 1 :

X Intercepts

: (2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sec (θ) - 1 :

Vertical

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

Extreme Points of

sec (θ) - 1 :

Minimum

(2 πn, 0),

Maximum

(π + 2 πn, - 2)

Popular Examples

y = cos (x + 1)

f(x)=sqrt(x),0<= x<= 4

f (x) = x, 0 \leq x \leq 4

f(x)=(4-2csc^2(x))/(csc^2(x))

f (x) = \frac{4 - 2 csc ^{2} ( x )}{csc ^{2} ( x )}

y = \frac{2 x - 1}{x + 2}

f(x)=(sin(pi-x)-sin(pi+x))/(sin(2pi+x))

f (x) = \frac{sin ( π - x ) - sin ( π + x )}{sin ( 2 π + x )}

Frequently Asked Questions (FAQ)

What is the f(θ)=sec(θ)-1 ?
The f(θ)=sec(θ)-1 is