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]
3 years ago
14

Please help? I’m super lost...

Mathematics
1 answer:
babunello [35]3 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
HELP PLS ILL MARK BRAINLIEST
Lunna [17]

Answer:

3rd one

Step-by-step explanation:

3 0
3 years ago
You install 638 feet of fencing along the perimeter of a rectangular yard. The width of the yard is 152 feet. What is the length
vovikov84 [41]

The length is 486

Step-by-step explanation:

638 subtract 152

6 0
3 years ago
Plsss hurrrry math test
Bezzdna [24]

Answer:

I believe its a trapezoid. Sorry if I'm wrong.

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Answer the question
dmitriy555 [2]
Pi is canceled out
so 3/4 x 180 = 135
hope it helps
3 0
3 years ago
Is -4 and -5 &lt;,&gt;,or =
hjlf

-4 is greater than -5

4 0
2 years ago
Other questions:
  • Which statements are correct regarding the properties of trapezoids?
    9·1 answer
  • Which expression are equivalent 10
    6·1 answer
  • Find the midpoint and length between each pair of points. (5,5) (-1,3)<br><br> PLEASE HELP!!
    9·1 answer
  • Find the measure of angle x
    12·2 answers
  • The area of a compact disc is 452 4/7 square centimeters. What is the diameter of a compact disc ? Use 22/7 as an approximation
    6·1 answer
  • Who won the race between the two balls of string
    15·1 answer
  • Choose the situation in which the use of approximate numbers is most appropriate.
    11·1 answer
  • 2x - 5y +10x - 2y + 3z solve.
    12·1 answer
  • PLEASE HELP, I don’t know how to do this...like at all
    11·1 answer
  • HELP I NEED THIS ASAP ILL GIVE BRAINLIST
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!