So I'm looking at a worked example in my textbook and it's showing me how to find the x-intercepts when sketching a trig graph. For example
y= sin (x + pi/4)
0= sin (x + pi/4)
So x + pi/4 = 0, pi, 2pi ----> x= -pi/4, 3pi/4, 7pi/4
My question is, where did the 0, pi and 2pi come from?
I tried doing the same approach for this question
y= 2sin2(x-pi/2) - 2 but it's not working out.
Instead, I did this
0 = 2sin 2(x-pi/2) - 2
1 = sin 2(x-pi/2)
sin^-1 (1) = 2(x-pi/2)
pi/2 = 2(x-pi/2)
Sin is positive in quadrants 1 and 2
2(x-pi/2) = pi/2, pi/2 + 2pi = 5pi/2
(x-pi/2) = pi/4, 5pi/4
x = 3pi/4 , 7pi/4
Could someone explain what I did differently from what the worked example did?
I feel like my way is alot more time consuming than the worked examples....
Sorry this is a mess!