okay, i learned Sine/Cosine functions (sine waves and stuff) a few days ago, but last day i learned Tangent. I understood the stuff in class "y=tan kx", and i know how to find the period: Pi/|b| but i was doing these questions: I know that "y= A tan B( x - C ) D", where A is the amplitude (vertical stretch for Tan), B affects the period, C is the phase shift, and D is the vertical shift. Well, im trying to do the questions above, and it just doesn't make sense when compared to the answers! #5 is simple, because theres no brackets, but for the other ones, im confused!

Good grief, I think my brain may explode. What have I learned today? That I don't remember a damn thing I learned in High School Math, despite the fact that I had an 89% when I finished.

Really, im no slouch in math, i got 93% in Math11, and i did pretty well the first few topics, but this is really screwing me up. I have no idea say, for #7 how they came up with a period of Pi/2! Phase shift okay it just says Pi/4, and since its MINUS, i move it to the right. But where the hell does the period come from? Theres no number where 'b' is supposda be for the equation of Pi/|b|!

i just started takin calc as a senior in high school. i don't ever remember learning to graph tangent...just cosine and sin...but i think i've got an idea of how it works and the period answer for 7 looks to be a typo....but of course....im not really sure

It's been 20 years since I thought about this stuff but it seems to me that all the questions are of the form y=tan ax+b. Since the period of tan x is pi, then the period of tan ax+b must be pi/|a| (as you stated). Just think of the function as cycling through its possible values a times faster so it must happen over a range that's 1/a times the original period. And then the +b part just shifts the curve left or right so your phase shift is just -b. I think the answers look wrong.

Nick, you made a typo in the first formula, it's: y = A tan B( x - C ) + D And let's assume that the "5" in the right column should read "6" instead... 4 - p: pi/3 , ps: +pi/3 5 - p: pi/2 , ps: 0 (error in textbook) 6 - p: pi , ps: -pi/3 (error in textbook) 7 - p: pi , ps: +pi/4 (error in textbook) 8 - p: pi , ps: +pi/2 9 - p: pi/2 , ps: +pi/2 (error in textbook) 10 - p: 2*pi , ps: -pi (error in textbook) 11 - p: pi/3 , ps: -pi/9 It's really unfortunate that there are so many errors in the key, but you will find out that this is sometimes the case. Don't trust the key, trust your logic! For example, it's fairly easy to see that 4 and 9 must have answers that look alike, 6, 7 and 8 as well...

I thought the period was 2 Pi as Pi is only half a rotation. Whoops, nevermind, this is Tangent, not Sin/Cos/Sec/Csc. Takes a few minutes to warm the old brain up for stuff like Trig. BTW,

ugh. this is depressing, I got an A1 in Maths and A2 in Additional Maths at O-Level, a B in Maths at A-Level, actually taught the stuff for a few months in my old school after I finished school before I entered university, and I can't remember a thing!