PLEASE HELP! 40 POINTS! All the problems are in the screenshot!
1 answer:
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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.
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.
This simplifies to
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:
and
Divide both sides by 2 in both of those equations to get that values of theta are:
b.
Take the inverse tangent of both sides:
Taking the inverse tangent of the tangent on the left leaves us with just 7a. This simplifies to
We look to the unit circle to find which values of <em>a</em> give us a tangent of 1. They are:
Dibide each of those equations by 7 to find that the values of alpha are:
c.
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:
We look to the unit circle to find the values of beta that give us the cosine of 1/2 and those are:
Divide each of those by 3 to find the values of beta are:
d.
Let's rewrite this in terms of a trig ratio that we are a bit more familiar with:
We are going to simplify this even further by flipping both fraction upside down to make it easier to solve:
Now we will take the inverse cos of each side (same as above):
We look to the unit circle one last time to find the values of alpha that give us a cosine of -1/2:
Dividing both of those equations by 3 gives us
And we're done!!!
Answer:
<em>The value 60 represents the speed of the vehicle the counselor is driving.</em>
Step-by-step explanation:
<u>Linear Function</u>
The linear relationship between two variables d and t can be written in the form
Where m is the slope (or rate of change of d with respect to t) and b is the y-intercept or the point where the graph of the line crosses the y-axis
The function provided in our problem is
Where d is the distance in miles the counselor still needs to drive after t hours. Rearranging the expression:
Comparing with the general form of the line we can say m=-60, b=130. The value of -60 is the slope or the rate of change of d with respect to t. Since we are dealing with d as a function of time, that value represents the speed of the vehicle the counselor is driving. It's negative because the distance left to drive decreases as the time increases