1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vadim26 [7]
2 years ago
14

Please help? I’m super lost...

Mathematics
1 answer:
babunello [35]2 years ago
8 0

Answer:

Step-by-step explanation:

In all of these problems, the key is to remember that you can undo a trig function by taking the inverse of that function.  Watch and see.

a.  sin2\theta =-\frac{\sqrt{3} }{2}

Take the inverse sin of both sides.  When you do that, you are left with just 2theta on the left.  That's why you do this.

sin^{-1}(sin2\theta)=sin^{-1}(-\frac{\sqrt{3} }{2} )

This simplifies to

2\theta=sin^{-1}(-\frac{\sqrt{3} }{2} )

We look to the unit circle to see which values of theta give us a sin of -square root of 3 over 2.  Those are:

2\theta =\frac{5\pi }{6} and

2\theta=\frac{7\pi }{6}

Divide both sides by 2 in both of those equations to get that values of theta are:

\theta=\frac{5\pi }{12},\frac{7\pi }{12}

b.  tan(7a)=1

Take the inverse tangent of both sides:

tan^{-1}(tan(7a))=tan^{-1}(1)

Taking the inverse tangent of the tangent on the left leaves us with just 7a.  This simplifies to

7a=tan^{-1}(1)

We look to the unit circle to find which values of <em>a</em> give us a tangent of 1.  They are:

7\alpha =\frac{5\pi }{4},7\alpha =\frac{\pi }{4}

Dibide each of those equations by 7 to find that the values of alpha are:

\alpha =\frac{5\pi}{28},\frac{\pi}{28}

c.  cos(3\beta)=\frac{1}{2}

Take the inverse cosine of each side.  The inverse cosine and cosine undo each other, leaving us with just 3beta on the left, just like in the previous problems.  That simplifies to:

3\beta=cos^{-1}(\frac{1}{2})

We look to the unit circle to find the values of beta that give us the cosine of 1/2 and those are:

3\beta =\frac{\pi}{6},3\beta  =\frac{5\pi}{6}

Divide each of those by 3 to find the values of beta are:

\beta =\frac{\pi }{18} ,\frac{5\pi}{18}

d.  sec3\alpha =-2

Let's rewrite this in terms of a trig ratio that we are a bit more familiar with:

\frac{1}{cos(3\alpha) } =\frac{-2}{1}

We are going to simplify this even further by flipping both fraction upside down to make it easier to solve:

cos(3\alpha)=-\frac{1}{2}

Now we will take the inverse cos of each side (same as above):

3\alpha =cos^{-1}(-\frac{1}{2} )

We look to the unit circle one last time to find the values of alpha that give us a cosine of -1/2:

3\alpha =\frac{7\pi}{6},3\alpha  =\frac{11\pi}{6}

Dividing both of those equations by 3 gives us

\alpha =\frac{7\pi}{18},\frac{11\pi}{18}

And we're done!!!

You might be interested in
(GEOMETRY HELP) Given right triangle JKL, what is the value of cos(L)?
Evgesh-ka [11]
The answer is 5
_
13
6 0
3 years ago
Read 2 more answers
Help please this is for my homework that is due to tomorrow!!
Murljashka [212]

The given polygons are similar

Step-by-step explanation:

By observing the given diagrams, we can see that the respective angles are congruent.

Two shapes are said to be similar if they have same shapes or one shape is created by uniformly increasing or decreasing the side of other.

For this purpose we find the scale factor of greater to smaller image, if the scale factor is same for each side then the two shapes are similar

So,

The scale factor is:

\frac{EF}{AB} = \frac{3}{1} = 3\\\\\frac{FG}{BC} = \frac{9}{3} = 3\\\\\frac{GH}{CD} = \frac{15}{5} = 3\\\\\frac{EH}{AD} = \frac{21}{7} = 3

We can see that the scale factor is same for all sides.

Hence,

The given polygons are similar

Keywords: Polygons, similarity

Learn more about polygons at:

  • brainly.com/question/6569012
  • brainly.com/question/6541303

#LearnwithBrainly

5 0
2 years ago
A bag contains 36 marbles. 10 marbles are green, 6 marbles are blue, 18 marbles are yellow, and 2 marbles are purple.
alexdok [17]

Answer:

10/72 or 0.14

Step-by-step explanation:

There are 72 marbles in total and 10 of them are green. So, it is 10/72 or 1.388 rounded to the nearest hundredth is 0.14.

7 0
2 years ago
(4.23)(1.6) please multiple
Wewaii [24]

Answer:

The correct answer is 6.768.

Step-by-step explanation:

(4.23)(1.6) = 6.768

8 0
2 years ago
Read 2 more answers
A rectangular, above-ground swimming
gregori [183]
The answer is A. 158 lbs
3 0
3 years ago
Other questions:
  • Make x the subject of h = 4(x + 3y) + 2<br><br> Plz help
    10·1 answer
  • 44^4 = 22^4 * ? find the missing factor in exponential form. How would you solve this?
    15·2 answers
  • D=c-s/n answer for n
    10·1 answer
  • A palm tree is supported by two guy wires as shown in the diagram below. Which trig expression can be used to find the height on
    8·1 answer
  • What’s the cube root shown
    5·2 answers
  • Solve the following equation for a. <br><br> a-f=q
    5·1 answer
  • Susan deposited $275 in a savings account that earns simple interest at a rate of 4.5%. She made no additional deposits and no w
    5·2 answers
  • Pls help, urgent!!!!! Will try to give brainliest
    12·2 answers
  • Construct a circle through points<br> X, Y, and Z.
    5·1 answer
  • Question 7 of 10
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!