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Digiron [165]
3 years ago
5

[Pre-Calc] Please Help! I don’t know where to start. How do I do this?

Mathematics
1 answer:
sertanlavr [38]3 years ago
3 0

Answer:

See Below.

Step-by-step explanation:

Problem A)

We have:

\displaystyle \csc^2\theta \tan^2\theta -1=\tan^2\theta

When in doubt, convert all reciprocal trig functions and tangent into terms of sine and cosine.

So, let cscθ = 1/sinθ and tanθ = sinθ/cosθ. Hence:

\displaystyle \left(\frac{1}{\sin^2\theta}\right)\left(\frac{\sin^2\theta}{\cos^2\theta}\right)-1=\tan^2\theta

Cancel:

\displaystyle \frac{1}{\cos^2\theta}-1=\tan^2\theta

Let 1/cosθ = secθ:

\sec^2\theta -1=\tan^2\theta

From the Pythagorean Identity, we know that tan²θ + 1 = sec²θ. Hence, sec²θ - 1 = tan²θ:

\tan^2\theta =\tan^2\theta

Problem B)

We have:

\sin^3x=\sin x-\sin x \cos^2 x

Factor out a sine:

\sin x(\sin^2 x)=\sin x-\sin x\cos^2 x

From the Pythagorean Identity, sin²θ + cos²θ = 1. Hence, sin²θ = 1 - cos²θ:

\sin x(1-\cos^2 x)=\sin x-\sin x\cos^2x

Distribute:

\sin x- \sin x \cos^2 x=\sin x-\sin x\cos^2 x

Problem C)

We have:

\displaystyle \frac{\cos 2x+1}{\sin 2x}=\cot x

Recall that cos2θ = cos²θ - sin²θ and that sin2θ = 2sinθcosθ. Hence:

\displaystyle \frac{\cos^2 x-\sin^2 x+1}{2\sin x\cos x}=\cot x

From the Pythagorean Identity, sin²θ + cos²θ = 1 so cos²θ = 1 - sin²θ:

\displaystyle \frac{2\cos^2 x}{2\sin x\cos x}=\cot x

Cancel:

\displaystyle \frac{\cos x}{\sin x}=\cot x

By definition:

\cot x = \cot x

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3x+5=4 two step equations
s344n2d4d5 [400]

Answer:

x = -1/3

Step-by-step explanation:

Move 5 to the other side of the equation

3x = 4-5

3x = -1

x = -1/3

7 0
3 years ago
Use the definition mtan=lim
Leokris [45]

(a) mtan refers to the slope of the tangent line. Given <em>f(x)</em> = 9 + 7<em>x</em> ², compute the difference quotient:

\dfrac{f(x+h)-f(x)}h = \dfrac{(9+7(x+h)^2)-(9+7x^2)}h = \dfrac{(9+7x^2+14xh+7h^2)-9-7x^2}h = \dfrac{14xh+7h^2}h

Then as <em>h</em> approaches 0 - bearing in mind that we're specifically considering <em>h</em> <em>near</em> 0, and not <em>h</em> = 0 - we can eliminate the factor of <em>h</em> in the numerator and denominator, so that

m_{\rm tan} = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0}\frac{14xh+7h^2}h = \lim_{h\to0}(14x+7h) = 14x

and so the slope of the line at <em>P</em> (0, 9), for which we take <em>x</em> = 0, is 0.

(b) The equation of the tangent line is then <em>y</em> = 9.

4 0
2 years ago
0.003 divided by 8.1
dusya [7]

2700  is your answer

Step-by-step explanation:

7 0
3 years ago
If a rope is 36 feet long and cut into 8 sections what is the length in feet of each section
tigry1 [53]

Answer:

The length of feet in each section is 4 4/8 which is then reduced to 4 1/2

Step-by-step explanation:

In order to get the answer, you will divided 36 by 8. When you divide, you then get 4 4/8 which is then reduced to 4 1/2. Hope this helps! :)


<h2>CloutAnswers</h2>
3 0
3 years ago
Read 2 more answers
What's bigger 2/3 or 4/5
Eduardwww [97]
The best thing to do is either to find a common denominator or convert them to decimals.
I will find a common denominator.
A common denominator of 3 and 5 is 15.
You multiply the first fraction by 5
2*5= 10
This then becomes 10/15
You then multiply the second by 3.
4*3= 12
Therefore, this becomes 12/15
As the second of these fractions is larger, this means that 4/5 is larger.
The alternative method is to put them into decimals, in which case 2/3= 0.66 and 4/5= 0.8
Hope this helps :) 
4 0
3 years ago
Read 2 more answers
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