Question

Would you show me that why (2k-1)pi to be 1/5pi(5k-2)?

Answer 1

Reading your attachment, the contention is not so much (2k-1)pi = 1/5pi(5k-2)
Each line should be taken individually, in the first line -3pi, -pi, pi, 3pi... this line continues in the positive direction and negative direction (2k-1)pi is a 'trick' or counting technique that keeps this line going continuously. Same thing on the other line. These techniques are taught in detail in courses like discrete math; they are introduced in courses like trig and cause great confusion.

Answer 2

actually it is not a question, it is my answer but i don't know why (2k-1) to 1/5pi(5k-2),
for the ori question please find second attachment

Answer 3

I'm showing why f(x) intersects these points

Answer 4

Well you've got the solution there. First you set f(x) equal to 0 because you're trying to find the x-intercepts.
1. Then minus 1 on both sides.
2. arccos both sides, which gives infinite answers which can be summarized as π(2k-1)
3. add pi/5 on both sides to get
π(2k-1) + π/5
=2kπ-π+π/5
=2kπ -4π/5
=(2π/5) (5k - 2)
4. Divide by 2 on both sides to get
(π/5) (5k-2)

Answer 5

why =2kπ -4π/5 =(2π/5) (5k - 2) ?