Question

Given that the terminal side of an angle theta is on the line y equals minus 3 over 4 x in the fourth quadrant, what is cos theta ?

a. minus 3 over 5
b. minus fraction numerator 4 over denominator square root of 5 end fraction
c.4 over 5
d. fraction numerator 4 over denominator square root of 5 end fraction

Answer 1

To find cos(theta), we use the coordinates on the terminal side of the angle and apply the Pythagorean theorem.

Step-by-step explanation:

To find the value of cos(theta), we need to determine the x-coordinate of a point on the terminal side of the angle theta. Since the terminal side is on the line y = (-3/4)x in the fourth quadrant, the x-coordinate will be positive and the y-coordinate will be negative.

Let's assume the x-coordinate is 4. Substituting this value into the equation y = (-3/4)x gives us y = (-3/4)(4) = -3.

Now, we can use the Pythagorean theorem to find the length of the hypotenuse. Using the values of x = 4 and y = -3, we have: A = sqrt(4^2 + (-3)^2) = sqrt(16 + 9) = sqrt(25) = 5.

Finally, we can calculate cos(theta) by dividing the adjacent side, which is 4, by the hypotenuse, which is 5.

cos(theta) = 4/5