Trig Identify Question

Question

Can someone explain why this:

f(x) = sin x + cos x

0 ≤ x ≤ 2𝜋

(a) Find the intervals on which f is increasing. (Enter the interval that contains smaller numbers first.)

( , ) ∪ ( , )

Find the interval on which f is decreasing.

( , ) (b) Find the local minimum and maximum values of f. (Round your answers to two decimal places.)

(max)

(min) (c) Find the inflection points.

( , ) (smaller x value)

( , ) (larger x value)

Find the interval on which f is concave up.

( , )

Find the intervals on which f is concave down. (Enter the interval that contains smaller numbers first.)

( , ) ∪ ( , )

FRIDAY22

Why does sin(x)-cos(x) =0 become 1- sinx/cosx???

Answer 1

one method is use a graphing calculator

such as Desmos online

graph sinx + cosx

max f(x) looks about 1.5 when x=about .8

min f(x) looks aobut -1.5 when x = about 4 or so

inflection points look about x=2.4 and 5.5

that's x values in radians

if you work the problem with calculus and trig, you should get answers similar but with a multiple of pi radians

y=sinx + cosx

y' = cosx - sinx = 0

divide by cosx

cosx/cosx - sinx/cosx = 0

1 -tanx = 0

tanx = 1

x = tan^-1(1) = 45 or 225 degrees

or pi/4 and 5pi/4 radians

the function's concavity changes at the infleciton points

the function is increasing from 0 to pi/4, then decreasing until 5pi/4, then increasing until 2pi