# Thread: Help with two trigonometry questions. (Sinusoidal)

1. ## Help with two trigonometry questions. (Sinusoidal)

Hello, I've been playing around with these two trigonometry problems in my notebook and I can't seem to solve them. Heres a link to problems and my answers, https://imgur.com/a/CYkY5.

Question 34 doesn't seem difficult to me, its when I get to the x-intercepts, Where is the function increasing? Where is the function decreasing? I'm not sure how to approach these since the diagram they included doesn't give me enough information on x axis to show what is what. For example the x-intercepts are 45, 135, 225 and 315 degrees, but I'm not sure if there right since I can't see the full axis. Is there a way to tell exactly what they are?

Question 35 has by far given me the most problems I think I tried about 5-8 times but I just don't seem to understand how to do it. When it states the x-intercept is 50 degrees does that mean it only touches up once and the reset is under? I'm just unaware on how to start.

2. ## Re: Help with two trigonometry questions. (Sinusoidal)

For #34 it seems clear to me that the x-intercepts are halfway between the numbered points on the x-axis. That is, x= (0+ 90)/2= 45, x= (90+ 180)/2= 135, x= (180+ 270)/2= 225, and (270+ 360)/2= 315. The function is increasing for x between 90 and 180 and for x between 270 and 360. The function is decreasing for x between 0 and 90 and for x between 180 and 270.

Problem 35 tells you that the domain is x between 0 and 180 so start by drawing a horizontal line representing the x-axis, marking one end 0, the other 180. Mark the center point, half way between the two end points, "90". Draw a second line, perpendicular to the first at the left end, representing the y-axis. Mark, lighter than the others since this is a "guide" not part of the actual graph, two horizontal lines at y= -5 and y= 1. You are told that the period is 360 but your graph only goes from 0 to 180, half of 360 so you are only drawing half a sine curve- the half above the center line. You are told that the amplitude is 3- you don't need to do anything for that, it just follows from what was said before, (1-(-5))/2= 3. You should draw another "guide" line, horizontal to the x-axis, at y= (1+ (-5))/2= -2, half way between -5 and 1. Finally, draw the actual graph: y= 0 at x approximately 50 (a little more than half way between 0 and 90), rises to 1 at x= 90+ 50= 140, a little more than half way between 90 and 180, then back down, to a little more than y= 0 at x= 180. You should also go back from x= 50 to x= 0, dropping down a little below the x-axis. You cannot, of course actually calculate any of those- the graph is only expected to be approximate.

3. ## Re: Help with two trigonometry questions. (Sinusoidal)

Thank you for the help, as for problem 35 I'm having some issues with it. I'm having issues where to put the points since the problem says "The function never increases" so wouldn't having a point at 1 again cause it to increase? Heres a picture of what I've drawn so far. https://imgur.com/a/FkJfk

4. ## Re: Help with two trigonometry questions. (Sinusoidal)

Originally Posted by Tyler010
Thank you for the help, as for problem 35 I'm having some issues with it. I'm having issues where to put the points since the problem says "The function never increases" so wouldn't having a point at 1 again cause it to increase? Heres a picture of what I've drawn so far. https://imgur.com/a/FkJfk
Yes, the problem says "The function never increases". It also says "the function decreases when 0< x< 180" and "the domain is $\displaystyle 0\le x\le 180$". So your function must start at y= 1 when x= 0 ("the y-intercept is 1"), cross the x- axis (y= 0) when x= 50 and continue down to y=-5 when x= 180.