Here is an expression: 2 + 3t

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 a 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

Reuben has scores of 70,75,83, and 80 on four spanish quizzes. what score must he get on the next quiz to achieve an average of

Sergio [31]

X - the score he must get

$\frac{70+75+83+80+x}{5} \geq 80 \\
\frac{308+x}{5} \geq 80 \\
308+x \geq 400 \\
x \geq 92$

He must get at least 92 points.

4 0

3 years ago

Read 2 more answers

Anthony is an executive assistant. He makes $15.85 per hour. If he worked 47.50 hours this week, what is his (a) OT pay? What ab

alexdok [17]

Anthony's OT pay will be $118.875 and his overall pay will be $752.875.

Number of hours Anthony has to work in a week = 5 × 8 = 40 hours.

He worked for = 47.50 hours.

Overtime = 47.50 hours - 40 hours = 7.50 hours

Pay per hour = $15.85 / hour

Overtime pay (OT pay) = $15.85 × 7.50 = $118.875

Overall pay = $15.85 × 47.50 = $752.875

Therefore, Anthony's OT pay is $118.875 and his overall pay is $752.875.

Learn more about overtime pay here -

brainly.com/question/19022439

#SPJ9

5 0

1 year ago

What is the end behavior of the function f(x) = 3x4−x3 + 2x2 + 4x + 5? (1 point)

ELEN [110]

Answer: both the left and right sides go to +∞

Step-by-step explanation:

End behavior can be determined by two things:

Sign of the leading coefficient
Degree of the function

Sign of leading coefficient:

positive: right side goes to +∞

negative: right side goes to -∞

⇒ Leading coefficient of this function is 3 so the right side goes to +∞

Degree (exponent of leading coefficient):

even: both the left and right sides point in the SAME direction

odd: the left and right sides point in OPPOSITE directions

⇒ Degree of this function is 4 so the left side will point in the same direction as the right side.

8 0

3 years ago

A figure has the following coordinates x (0,1).Y (4,6) z (-5,-1). If the figure is translates 4 units left and 3 units up, what

iVinArrow [24]

Answer:

z' (-9,2)

Step-by-step explanation:

I recomend using desmos to show the relashinship

If you don't want to, thwn do this

Preimage $(0-4,1+3),(4-4,6+3),(-5-4,-1+3)$

Since we are finding z, we only use the final cordinates

z'=(-9,2)

8 0

2 years ago