Find the equation of the linear function represented by the table below in slope-intercept form.
1 answer:
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Answer:
44°
Step-by-step explanation:
The reference angle is the magnitude of the smallest angle between the terminal ray and the x-axis.
Your angle is one full circle clockwise plus 44° more (-360° -44° = -404°), so makes an angle of -44° with respect to the positive x-axis. The magnitude of that is 44°.
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<em>Using a function</em>
The attachment shows a calculator function that can be used to find the reference angle for any angle. (Replace the value -404 with the angle of your choice.)
<h3>Answer: 5</h3>
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One method is to plot the points P(3,6) and Q(7,3) on the same xy grid. Plot a third point R at (3,3). See the diagram below.
A right triangle forms in which we can find the legs PR = 3 and RQ = 4. The hypotenuse is found through the pythagorean theorem.
a^2+b^2=c^2
3^2+4^2 = c^2
9+16 = c^2
c^2 = 25
c = sqrt(25)
c = 5
This is the length of PQ
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Or you can use the distance formula which is effectively using the pythagorean theorem just in a slightly different format (though it may not be obvious).
The given function is
The general form of the cosine function is
a is the amplitude
2pi/b is the period
c is the phase shift
d is the vertical shift
By comparing the two functions
a = 4
b = pi
c = 0
d = 1
Then its period is
The equation of the midline is
Since the maximum is at the greatest value of cos, which is 1, then
Since the minimum is at the smallest value of cos, which is -1, then
Then substitute them in the equation of the midline
The answers are:
Period = 2
Equation of the midline is y = 1
Maximum = 5
Minimum = -3