I don't understand this at all!<br>HELPP!!

babunello [35]

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!!!

8 0

2 years ago

Help please ASAP

Nat2105 [25]

41. A

42. A

43. B

44. B

45. A

46. A

47. B

48. A

49. A

50. A

51. B

52. B

6 0

3 years ago

Find the sum of a finite geometric sequence from n = 1 to n = 8, using the expression −2(3)^n − 1.

Kazeer [188]

The sum if the geometric sequence given by:
an=-2(3)^(n-1)
will be:
when:
n=1
an=-2
when n=2
a2=-6
when n=3
a3=-18

when n=4
a4=-54

when n=5
a5=-162

when n=6
a6=-486

when n=7
a7=-1458

when n=8
a8=-4374

thus the summation of the term will be:
Sn=(-4374+-1458+-486+-162+-54+-18+-6+-2)
Sn=-6560
the answer is -6560

6 0

3 years ago

Line KL has an equation of a line y = 4x + 5. Which of the following could be an equation for a line that is perpendicular to li

djyliett [7]

To find a perpendicular slope (or line), the slope (in this case 4x) must be the opposite sign and its reciprocal, which is basically the fraction flipped upside down. Since 4 is technically 4/1, that fraction flipped is 1/4. And since you need to flip the sign too, instead of it being a positive number, it's negative. Your answer is -1/4x-8

3 0

3 years ago

Read 2 more answers

Michelle, lori, and patti buy lunch together. The total bill was $45. If michelle pays 35% of the total bill and lori pays 48% o

siniylev [52]

Answer:

$7.65

Step-by-step explanation:

step one:

The total bill was $45.

michelle pays 35% of the total bill

= 35/100*45

=0.35*45

=$15.75

lori pays 48% of the bill

= 48/100*45

=0.48*45

=$21.6

Therefore patti will pay

=45-15.75-21.6

=$7.65

3 0

3 years ago

Read 2 more answers

I don't understand this at all!HELPP!!​

I don't understand this at all!HELPP!!