I learned this 4 months ago and now I forgot how to do it.....

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

3 years ago

Jane and Nancy were both awarded National Merit Scholarships (for academic excellence), and both love mathematics. Jane breezed

Scorpion4ik [409]

Answer:

c. Inductive and Strong

Step-by-step explanation:

In inductive reasoning, provided data is analyzed in order to reach a conclusion. In this case, the argument provides data regarding Jane and Nancy's awards and their love for mathematics and then draws a conclusion regarding Nancy's performance in a particular class, this is an example of inductive reasoning.

As for the strength of the argument, it is plausible to infer that Jane and Nancy have similar mathematics skills since they both love calculus and excel academically. Therefore, if Jane does well in the calculus class, it is a strong argument to say that Nancy does as well.

The answer is :

c. Inductive and Strong

8 0

3 years ago

The X- and y-coordinates of point P are each to be chosen at random from the set of integers 1 through 10.

bagirrra123 [75]

Answer:

Ok, as i understand it:

for a point P = (x, y)

The values of x and y can be randomly chosen from the set {1, 2, ..., 10}

We want to find the probability that the point P lies on the second quadrant:

First, what type of points are located in the second quadrant?

We should have a value negative for x, and positive for y.

But in our set; {1, 2, ..., 10}, we have only positive values.

So x can not be negative, this means that the point can never be on the second quadrant.

So the probability is 0.

3 0

3 years ago

Solve by elimination.<br> 5x-7y=19<br> 7x-7y=-7

SVEN [57.7K]

Answer:

(x,y)=(-13,-12)

Step-by-step explanation:

5x - 7y = 19

7x - 7y = -7 Multiply both sides of the equation by -1

Which then gives you :

5x-7y=19 Sum the equations vertically to eliminate

-7x+7y=7 at least on variable

-2x=26 Divide both sides of the equation by -2

X=-13 Substitute the given value of x into the equation 7x - 7y =-7

7 x(-13)-7y=-7 solve the equation for y

y=-12

Thus gives you (-13,-12)

Hope this was useful!!! Sorry if it's wrong.

4 0

3 years ago

There are two spinners. Each spinner has 10 equal sectors labeled with the numbers 1 through 10.

Reika [66]

Answer: Second option is correct.

Step-by-step explanation:

Since we have two spinners,

Each spinner has 10 equal sectors labeled with the numbers from 1 to 10.

Primes numbers from 1 to 10 is given by

$\{2,3,5,7\}$

So, number of outcomes shows a primes number from 1 to 10 = 4

Similarly ,

Composite numbers from 1 to 10 is given by

$\{4,6,8,9,10\}$

So, number of outcomes shows a composite number from 1 to 10 =5

∴ Total outcomes show a prime number on the first spinner and a composite number on the second spinner is given by

$4\times 5=20\\$

Thus, Second option is correct.

3 0

3 years ago