The point P(-11.00, -3.00) is on the terminal arm of an angle in standard position. Determine the exact values of the cosine ratio.
The answer should be rounded to two decimal places.
x = -11
y = -3
r = √130
cosθ = x/r = -11/√130
You've posted a bunch of these. How about you show your work next time? Surely you have the idea by now.
and don't say you want an exact value, and then ask that it be rounded to two decimal places. You want it exact, or not?
You're absolutely right sir!
Next time, I will use this site not to just ask a question but to also confirm if my work correct!
To determine the exact value of the cosine ratio of an angle, we need to first identify the quadrant in which the angle lies.
Given that point P(-11.00, -3.00) is on the terminal arm of the angle, we can find the angle's reference angle by using the inverse tangent function:
reference angle = tan^(-1)(y / x)
Plugging in the values for x and y, we get:
reference angle = tan^(-1)(-3.00 / -11.00)
Using a calculator, we find that the reference angle is approximately 16.55 degrees.
Since point P lies in the third quadrant (where x < 0 and y < 0), the angle's actual value can be found by subtracting the reference angle from 180 degrees:
angle = 180 - reference angle
= 180 - 16.55
= 163.45 degrees
Finally, to find the cosine ratio of the angle, we can use the cosine function:
cosine ratio = cos(angle)
Using a calculator, we find that the cosine ratio of the angle is approximately -0.9848.
Therefore, the exact value of the cosine ratio for the given angle is -0.9848 (rounded to two decimal places).