The graph of y = x and y = cos x is shown below. (y = x is in black and y = cos x is in red)

The solution of cos x = x has to be determined.

cos x = x

=> cos x - x = 0

For x = 0.7

cos x - x = 0.0648

for x = 0.8

cos x - x = -0.1032

By the intermediate value theorem a solution of cos x = x lies in the interval (0.7, 0.8)

This can be seen when f(x) = cos x - x is plotted.

It is seen that the graph crosses the x-axis at a value of x lying between 0.7 and 0.8.

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now