What is the reference angle for cos 2pie/3

Step-by-step explanation:

If your mind works better in degrees than it does radians, as does mine, it will be beneficial to us to see what degree measure this angle is. Convert it to degrees using the fact that 180° = π:

degrees

Now that we know that, we can plot that angle in a coordinate plane. The terminal side of the angle lands in quadrant 2. To find the reference angle, we subtract 120 from 180 and get that the reference angle is 60 degrees, which is the same as π/3.

Answers:

This forms the equation 1x-5y = -15, which is the same as x-5y = -15

Explanation:

Let's find the slope. I'll pick the first two rows to form the two points needed

(x1,y1) = (0,3)

(x2,y2) = (10,5)

These are then plugged into the slope formula.

m = slope

m = (y2-y1)/(x2-x1)

m = (5-3)/(10-0)

m = 2/10

m = 1/5

m = 0.2

The y intercept is b = 3 since this is the y value when x = 0.

With m = 0.2 and b = 3, we go from y = mx+b to y = 0.2x+3

Let's multiply both sides by 5 to turn that decimal value into a whole number. I'm picking 5 since 0.2 = 1/5

So we get

y = 0.2x+3

5y = 5*(0.2x+3)

5y = 5*0.2x+5*3

5y = x+15

Now let's get x and y together, but move that 15 to its own side

5y = x+15

x+15 = 5y

x = 5y-15

x-5y = -15

This is one way to write the equation in standard form.

Standard form is Ax+By = C, where A,B,C are integers. Some math textbooks insist that A > 0. In this case, A = 1, B = -5, and C = -15.

As a way to check, we can plug in (x,y) = (15,6) from the third row of the table to see that..

x-5y = -15

15-5(6) = -15

15 - 30 = -15

-15 = -15

This verifies the third row. I'll let you check the first two rows of the table to fully confirm this equation works.