Which value for x is a solution to cosx = sqrt of 2/2?

a) -9pi/4
b) 3pi/4
c) -3pi/4
d) 4pi/3

What is the first step I should do?

45 degrees in quadrant 1 or 4

45 degrees = pi/4

-9 (pi/4) is -pi/4 which is 45 degrees in Q 4

Well, the first step is finding a good spot to sit down and get comfy. Solving equations can be a bit of a journey, so it's important to be in a relaxed state of mind. Once you're all settled in, we can start tackling this problem!

To find the value for x that is a solution to the equation cos(x) = √2/2, you should start by taking the inverse cosine (arc cosine) of both sides of the equation.

The first step to solve the equation cos(x) = √2/2 is to find the angles or values of x where the cosine function equals √2/2. To do this, we can recall the special angles in the unit circle where the cosine function takes on certain values.

The special angles that have a cosine value of √2/2 are 45 degrees and 315 degrees (or π/4 and 7π/4 in radians). This is because at these angles, the x-coordinate on the unit circle is equal to √2/2.

Therefore, to solve the equation cos(x) = √2/2, we need to find the values of x that are equal to 45 degrees or 315 degrees in radians. The answer choices given are -9π/4, 3π/4, -3π/4, and 4π/3 in radians.

To determine the correct solution, we can compare the answer choices to the values of 45 degrees and 315 degrees in radians. Let's analyze each option:

a) -9π/4 = -2.25π: This is not equal to 45 degrees or 315 degrees; hence, it is not a valid solution.

b) 3π/4 = 0.75π: This is equivalent to 45 degrees in radians, so it is a valid solution.

c) -3π/4 = -0.75π : This is equivalent to -45 degrees or 315 degrees; hence, it is a valid solution.

d) 4π/3 ≈ 1.33π: This is not equal to 45 degrees or 315 degrees; thus, it is not a valid solution.

Therefore, the values of x that are solutions to the equation cos(x) = √2/2 are b) 3π/4 and c) -3π/4.