Pi/4 radians
You're looking for the angle that has a secant of sqrt(2). And since the secant is simply the reciprocal of the cosine, let's take a look at that.
sqrt(2) = 1/x
x*sqrt(2) = 1
x = 1/sqrt(2)
Let's multiply both numerator and denominator by sqrt(2), so
x = sqrt(2)/2
And the value sqrt(2)/2 should be immediately obvious to you as a trig identity. Namely, that's the cosine of a 45 degree angle. Now for the issue of how to actually give you your answer. There's no need for decimals to express 45 degrees, so that caveat in the question doesn't make any sense unless you're measuring angles in radians. So let's convert 45 degrees to radians. A full circle has 360 degrees, or 2*pi radians. So:
45 * (2*pi)/360 = 90*pi/360 = pi/4
So your answer is pi/4 radians.
Answer:
A) A[p(t)] = 36πt²
B) 7234.56 square units
Step-by-step explanation:
<u>Given functions</u>:
<u>Part A</u>
To find the area of the circle of spilled paint as a function of time, substitute the function p(t) into the given function A(p):
<u>Part B</u>
Given
Substitute the given values into the equation for A[p(t)} found in part A:
Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.
<h3>
Answer: Approximately 13 square units (choice B)</h3>
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Explanation:
The given reflex angle is 215 degrees. A reflex angle is anything over 180 degrees, but less than 360. Subtract 215 from 360 to get the measure of angle AOB
angle AOB = 360 - 215 = 145
angle AOB = 145 degrees
We'll use this later.
Now find the area of the full circle. Use the formula A = pi*r^2. The radius is r = sqrt(10) which can be found through the distance formula or the pythagorean theorem. You want to find the length of either OA or OB to get the radius.
The area of the circle is
A = pi*r^2
A = pi*(sqrt(10))^2
A = 10pi
This is the exact area of the full circle, but we want just a fractional portion of it. Specifically we want the pie slice that is formed by angle AOB
area of sector AOB = [ (angle AOB)/360 ] * (area of full circle)
area of sector AOB = (145/360)*10pi
area of sector AOB = 145pi/36
area of sector AOB = 145*3.14/36
area of sector AOB = 12.647 approximately
area of sector AOB = 13 square units approximately, after rounding to the nearest whole number