en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y=3cos(x+pi/3)-1

Solution

y = 3 cos (x + \frac{π}{3}) - 1

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - 4 \leq f (x) \leq 2

X Intercepts : (arccos (\frac{1}{3}) - \frac{π}{3} + 2 πn, 0), (2 π - arccos (\frac{1}{3}) - \frac{π}{3} + 2 πn, 0), Y Intercepts : (0, \frac{1}{2})

Asymptotes : None

Extreme Points : Minimum (\frac{2 π}{3} + 2 πn, - 4), Maximum (\frac{5 π}{3} + 2 πn, 2)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 4, 2]

Solution steps

Periodicity of

3 cos (x + \frac{π}{3}) - 1 : 2 π

Domain of

3 cos (x + \frac{π}{3}) - 1 : - \infty < x < \infty

Range of

3 cos (x + \frac{π}{3}) - 1 : - 4 \leq f (x) \leq 2

Axis interception points of

3 cos (x + \frac{π}{3}) - 1 :

X Intercepts

: (arccos (\frac{1}{3}) - \frac{π}{3} + 2 πn, 0), (2 π - arccos (\frac{1}{3}) - \frac{π}{3} + 2 πn, 0),

Y Intercepts

: (0, \frac{1}{2})

Asymptotes of

3 cos (x + \frac{π}{3}) - 1 :

None

Extreme Points of

3 cos (x + \frac{π}{3}) - 1 :

Minimum

(\frac{2 π}{3} + 2 πn, - 4),

Maximum

(\frac{5 π}{3} + 2 πn, 2)

Popular Examples

f(θ)=sec(θ)+csc(θ)

f (θ) = sec (θ) + csc (θ)

f (θ) = 9 cos (θ)

y = \frac{x + 5}{x - 6}

y= 1/(cot(x)+1)+1/(tan(x)+1)

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

y = x^{2} + x + 5

Frequently Asked Questions (FAQ)

What is the y=3cos(x+pi/3)-1 ?
The y=3cos(x+pi/3)-1 is