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slega [8]
3 years ago
15

Is the answer I choose right and if not please tell me what it is Nd Please tell me how to show the work also !

Mathematics
2 answers:
romanna [79]3 years ago
6 0

Answer:

yes

Step-by-step explanation:

Aliun [14]3 years ago
4 0
Yes the answer you chose is correct
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CALCULUS - Find the values of in the interval (0,2pi) where the tangent line to the graph of y = sinxcosx is
Rufina [12.5K]

Answer:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

Step-by-step explanation:

We want to find the values between the interval (0, 2π) where the tangent line to the graph of y=sin(x)cos(x) is horizontal.

Since the tangent line is horizontal, this means that our derivative at those points are 0.

So, first, let's find the derivative of our function.

y=\sin(x)\cos(x)

Take the derivative of both sides with respect to x:

\frac{d}{dx}[y]=\frac{d}{dx}[\sin(x)\cos(x)]

We need to use the product rule:

(uv)'=u'v+uv'

So, differentiate:

y'=\frac{d}{dx}[\sin(x)]\cos(x)+\sin(x)\frac{d}{dx}[\cos(x)]

Evaluate:

y'=(\cos(x))(\cos(x))+\sin(x)(-\sin(x))

Simplify:

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

Since our tangent line is horizontal, the slope is 0. So, substitute 0 for y':

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

Now, let's solve for x. First, we can use the difference of two squares to obtain:

0=(\cos(x)-\sin(x))(\cos(x)+\sin(x))

Zero Product Property:

0=\cos(x)-\sin(x)\text{ or } 0=\cos(x)+\sin(x)

Solve for each case.

Case 1:

0=\cos(x)-\sin(x)

Add sin(x) to both sides:

\cos(x)=\sin(x)

To solve this, we can use the unit circle.

Recall at what points cosine equals sine.

This only happens twice: at π/4 (45°) and at 5π/4 (225°).

At both of these points, both cosine and sine equals √2/2 and -√2/2.

And between the intervals 0 and 2π, these are the only two times that happens.

Case II:

We have:

0=\cos(x)+\sin(x)

Subtract sine from both sides:

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

Again, we can use the unit circle. Recall when cosine is the opposite of sine.

Like the previous one, this also happens at the 45°. However, this times, it happens at 3π/4 and 7π/4.

At 3π/4, cosine is -√2/2, and sine is √2/2. If we divide by a negative, we will see that cos(x)=-sin(x).

At 7π/4, cosine is √2/2, and sine is -√2/2, thus making our equation true.

Therefore, our solution set is:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

And we're done!

Edit: Small Mistake :)

5 0
2 years ago
Name two pairs of congruent angles.
larisa [96]

ZOSP= PSQ and

ZPSQ E ZOSR

4 0
2 years ago
PLZ HELP ASAP<br><br>The scale factor of ____ was applied to the first triangle
pashok25 [27]

The scale factor of 4 was applied to the first triangle. 6 was divided by 4 to get 1.5

5 0
3 years ago
find the simple interest earned when the principal is $500 at a rate of 10% held in the bank for 8 months
olga nikolaevna [1]

The Simple interest will be "$400".

Given values are:

  • Principle, P = $500
  • Interest rate, R = 10%
  • Time, T = 8 months

As we know,

→ Simple \ interest (SI) = \frac{P\times R\times T}{100}

By substituting the values, we get

→                                  =\frac{500\times 10\times 8}{100}

→                                  =5\times 10\times 8

→                                  = 400 ($)

Thus the above response is correct.  

Learn more about Simple interest here:

brainly.com/question/15469221

3 0
3 years ago
PLEASE HELP ME!!!!!!!
adell [148]

Answer:

A. 50.24

Step-by-step explanation:

f(4) = 3.14 times 4²

f(4) = 3.14(16)

f(4) = 50.24

<h2><u><em>xoxo, </em></u></h2><h2><u><em>your highness...</em></u></h2>
4 0
3 years ago
Read 2 more answers
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