Calculus Question

Question

Find the solution set of 3 (sec x – 1) = 5 – sec x in the interval 0 ≤ x < 2π , or when a table or calculator is used, in the interval 0° ≤ x < 360°.

What is the second from the last step?

a. sec x = 1

b. sec x = 4

c. sec x = 2

My answer was b.

What are the answers?

a. π/3 and 2π/3

b. π/6 and 11π/6

c. n/3 and 5π/3

My answer is c

Answer 1

3(sec x - 1) = 5 - sec x

3sec x - 3 = 5 - sec x

4sec x = 8

sec x = 2

So the second to the last step is sec x = 2.

Then solve sec x = 2.

This is the same as cos x = 1/2.

cos x = 1/2 between x = 0 and 2pi is when x = pi/3 and 5pi/3