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1 year ago

What are the domain and range of y=cot x? Select one choice for domain

Mathematics

1 answer:

Lostsunrise [7]1 year ago

4 0

The domain is $\boxed{x \neq n\pi}$ , where n is an integer.

This is because cot x = 1/tan(x), and if tan x = 0, then the fraction is undefined.

The range is all real numbers.

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Prove: cot(x) sec^4(x) = cot(x) +2tan(x) + tan^3(x)

masha68 [24]

$\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\qquad\qquad 
sec(\theta)=\cfrac{1}{cos(\theta)}\quad\qquad 1+tan^2(\theta)=sec^2(\theta)\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}
\qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\\\\
-------------------------------\\\\
cot(x)sec^4(x)=cot(x)+2tan(x)+tan^3(x)\\\\
-------------------------------\\\\$

$\bf \textit{so, let's do the left-hand-side}\\\\
cot(x)sec^2(x)sec^2(x)\implies cot(x)[1+tan^2(x)][1+tan^2(x)]
\\\\\\
cot(x)[1^2+2tan^2(x)+tan^4(x)]
\\\\\\
cot(x)+2tan^2(x)cot(x)+tan^4(x)cot(x)
\\\\\\
cot(x)+2\cdot \cfrac{sin^2(x)}{cos^2(x)}\cdot \cfrac{cos(x)}{sin(x)}+\cfrac{sin^4(x)}{cos^4(x)}\cdot \cfrac{cos(x)}{sin(x)}
\\\\\\
cot(x)+2\cdot \cfrac{sin(x)}{cos(x)}+\cfrac{sin^3(x)}{cos^3(x)}\implies \boxed{cot(x)+2tan(x)+tan^3(x)}$

8 0

3 years ago

Solve |x|+7<4 A. 0 B. {x|x<-11 or x>-3} C. {x|-3

mars1129 [50]

Answer:

{3xl42}

Step-by-step explanation:

3 0

2 years ago

Write the equation of the line in slope-intercept form that goes through the points: (2,4) and (7,-1)

IgorC [24]

Answer:

y= -x+8

Step-by-step explanation:

slope int. form: y=mx+b

first, we need to find the slope (m)

the two points are (2,4) and (7,-1).

to find the slope we do (y2-y1)/(x2-x1)

doing this we get -5/5=-1

now we can plug in point (2,4) and the slope into y=mx+b

doing this we get:

4=-1(2)+b

4=-2+b

b=8

now we have the equation:

y= -x+8

7 0

3 years ago

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d1i1m1o1n [39]

Answer:

x = input

y = output

y = 8 + x

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3 years ago

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weeeeeb [17]

I’m pretty sure that the answer 783 :)

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