Which of the following is a solution of 2cos^2x-cost-1=0 a. 0 degrees b. 150 degrees c. 180 degrees d. 210 degrees

{0, 150} degrees

Step-by-step explanation:

Given 2cos^2x-cost-1=0, let's simplify this problem by temporarily replacing cos x with y:

2y^2 - y -1 = 0

This can be solved by factoring:  (2y + 1)(y - 1) = 0.  From this we get two solutions:  y = -1/2 and y = 1.

Remembering that we let y = cos x, we now solve:

cos x = -1/2 and cos x = 1.

Note that cos x = 1 when x = 0 and the "adjacent side" coincides with the hypotenuse.

cos x = -1/2 when the hypotenuse is 2 and the "adjacent side" is -1.  This has two solutions between 0 and 360 degrees:  150 degrees and  270 degrees.

Four answer choices are given.  Both (a) (0 degrees) and (b) (150 degrees) satisfy the original equation.  Thus, the solution set is {0, 150} (degrees).

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a