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Serga [27]
3 years ago
12

Simplify sin Θ/√1-sin^2 Θ

Mathematics
2 answers:
dedylja [7]3 years ago
4 0
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2862279

_______________


Simplify the trigonometric expression.

Call the expression E:

\mathsf{E=\dfrac{sin\,\theta}{\sqrt{1-sin^2\,\theta}}\qquad\qquad(but~~1-sin^2\,\theta=cos^2\,\theta)}\\\\\\
\mathsf{E=\dfrac{sin\,\theta}{\sqrt{cos^2\,\theta}}}\\\\\\
\mathsf{E=\dfrac{sin\,\theta}{\left|cos\,\theta\right|}}}


\mathsf{E}=\left\{\!\begin{array}{rl}\mathsf{\dfrac{sin\,\theta}{cos\,\theta}\,,}&\mathsf{\quad if~~cos\,\theta>0}\\\\\mathsf{\dfrac{sin\,\theta}{-\,cos\,\theta}\,,}&\mathsf{\quad if~~cos\,\theta


So basically E is equivalent to \pm\,\mathsf{tan\,\theta}, where the sign depends on which quadrant \theta lies. Shortly,

\mathsf{\dfrac{sin\,\theta}{\sqrt{1-sin^2\,\theta}}}=\left\{\!
\begin{array}{rl}
\mathsf{tan\,\theta,}&\mathsf{\quad if~\theta~lies~either~in~the~1^{st}~or~the~4^{th}~quadrant}\\\\
\mathsf{-\,tan\,\theta,}&\mathsf{\quad if~\theta~lies~either~in~the~2^{nd}~or~the~3^{rd}~quadrant}
\end{array}


I hope this helps. =)


Tags:  <em>simplify trigonometric trig expression sine cosine tangent sin cos tan absolute value modulus trigonometry</em>

Tema [17]3 years ago
3 0

Answer:

\tan\theta

Step-by-step explanation:

We are given our expression as

\frac{\sin\theta}{\sqrt{1-\sin^{2}\theta}}

Here we have to recall the trignometric identities which says

\sin^{2}\theta + \cos^{2}\theta=1

taking \sin^{2}\theta to the right hand side of =

\cos^{2}\theta = 1- \sin^{2}\theta

Hence we replace 1- \sin^{2}\theta with \cos^{2}\theta in our main equation,

\frac{\sin\theta}{\sqrt{\cos^{2}\theta}}\\\frac{\sin\theta}{\cos\theta}\\=\tan\theta

Hence the answer is \tan\theta

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two friends bought a $14 pizza. Each person bought their own drink. The total cost of the food can be represented by the express
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We can just divide 2x+14 by 2 to get the cost of one person, as the equation represents the total costs of two people.

So the equation is x+7, but it may be x+14 because you can’t split the pizza.

I hope this helps!
4 0
3 years ago
-91÷13= <br><br>-3/7÷9/4=<br><br>-12÷-0.03=
Cloud [144]

Answer:

-7

-4/21

400

Because 13 times 7 is 91..so -7

-3/7÷9/4 becomes -3/7×4/9. Taking LCM and solving gives -4/21.

last is easy.it becomes (12÷3)×100=400

4 0
3 years ago
Ed buys a box of eggs costing £2.20, two packs of bacon for £2.80 each and two tins of baked beans.
Vika [28.1K]

Solving a linear equation, we can conclude that each tin costs £0.75

<h3>How much does a tin of beans cost in pounds?</h3>

First, we know that Ed buys one box of eggs for £2.20.

Also two packs of bacon for £2.80 each.

And two tins of beans for X each.

Then the total cost is:

C =  £2.20 + 2*£2.80 + 2*X

Now, we also know that when he pays with £10, he gets a change of £0.70.

Then we can solve the linear equation:

£10 - (£2.20 + 2*£2.80 + 2*X) = £0.70

£2.20 - 2*X = £0.70

£2.20 - £0.70 = 2*X

£1.50 = 2*X

£1.50/2 = X = £0.75

In this way, we can conclude that each tin costs £0.75

If you want to learn more about linear equations:

brainly.com/question/1884491

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4 0
1 year ago
The average price of homes sold in the U.S. in the past year was $220,000. A random sample of 81 homes sold this year showed a s
Molodets [167]

Answer:

We conclude that there has been a significant decrease in the average price homes.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $220,000

Sample mean, \bar{x} = $210,000

Sample size, n = 81

Significance level, α = 0.051

Population standard deviation, σ =  $36,000

First, we design the null and the alternate hypothesis

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We use One-tailed z test to perform this hypothesis.

Formula:

z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{210000 - 220000}{\frac{36000}{\sqrt{81}} } = -2.5

Calculating the p-value from the z-table, we have:

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Since,  

P-value < Significance level

We reject the null hypothesis and accept the alternate hypothesis. Thus, there has been a significant decrease in the average price homes.

5 0
3 years ago
2+2 <br> CORECT ANSWER <br> It is not easy so don’t think it is 2+2
liubo4ka [24]

Answer:

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Have a great day :}

8 0
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