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!

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1 Answer

Best answer

You're correct. What was the answer?

The only thing I would have done differently is say pi/2 is the only solution for sin(..) = 1 for a full period. You can add/subtract the periods later (2pi). But the only reason why you might be wrong is due to the domain and hence how many times you need to replicate the answer with an extra period.

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I got the right answer, I just wanted to check if my method was the best one to go about doing these questions.
When sketching trig graphs with translations (i.e. left or right), would you say the best way to go about sketching this is to sketch a basic graph without the translations, and then sketch the one with translations by moving it left or right?
Or would you say solving for solutions of the translated graph and then just sketching the translated graph is the best method?
There are many methods to solve trig questions, and they are usually all valid/equally good, so I wouldn't worry about it unless you're getting things wrong, in which case there's just a step in the process you've done wrong (which we can diagnose here if you get stumped). Re: Translations - this is a separate question, but once again there is no preferred solution. Do what is easier for you. I tend to do a hybrid approach where I solve for the points to get an "anchor" of where I know the graph goes through, then I visualise the "non-translated" curve and translate it to fit into the intercepts I've solved for.