Use the rated acute angle to state an equivalent expression
Tan110
The answer is tan290. Why isn't it 70? Please explain
tan 110 is negative (-2.75)
tan 70 is positive ( +2.75)
to have negatve tangent the angle must be in quadrants 2 or 4
tan 290 = -2.75 same as tan 110
How would you figure it out using a Cartesian plane?
And assuming you didn't know the answer was tan290, how would you get tan290 (because I'm supposed to arrive at the answer without knowing the answer..)?? Because the question is just asking for the equivalent expression of tan110, I just got tan70, which is why I wanted to know why that didn't work.
Okay, that seems really confusing. So in essence, I really just want to know how to find the equivalent expression using the related acute angle, tan110
Sorry, I still don't understand... I know I seem really dumb right now, but this unit just isn't working for me for some reason.. I'm usually pretty decent at math. We just started grade 11 trig and I'm totally lost after the first lesson.
I understand that it's in quadrant four, but how did you know that tan110 was equal to tan290? I mean, if I never told you the answer was tan290, how would you have arrived at the answer? I'm sure you wouldn't just do it by trial and error. I feel like I'm just missing a really simple concept here...
90 + 20 = 110
90 - 20 = 70
270 - 20 = 250
270 + 20 = 290
Preferably in terms of a Cartesian plane.
I gave you the plane
110 is in quadrant 2
x - negative, y is positive
you need the other quadrant where x and y have opposite signs
that is quadrant 4 where x is positve and y is negative
sketch it on your x y plane !
I did 20 degrees off the y axis in all four quadrants. The tan is negative in quadrants 2 and four
I could have done 70 degrees off the x axis in all four quadrants just as well.
Ohhh. Wow, I finally get it, haha. Thank you!! I honestly just have one more question... 5 minutes;
Great, makes my evening !
These concepts are not easy. However if you have been using them for 59 years they seem clear and therefore hard to explain.
Okay, so, I uploaded a picture of a portion of my notes which I don't understand; it's what I meant when I asked my question about how the sin, cos, and tan of the principal angle is equal to the sin, cos, and tan of the related acute angle.
imageshack.us/f/90/imgoc.png/
I don't know if you'll be able to understand. /:
If you can make out example 2 (the image enlarges) it's basically saying that angle 150's ratios are equal to angle 30's ratios...? Basically, that you can find the ratios of the principal angle using the related acute angle?
Sure, just like we were doing with your 110 degree problem.
That is 20 degrees from the y axis or 70 degrees from the x axis in quadrant 2
draw the other three lines that are 20 degrees from y and 70 degrees from x axes in the other three quadrants.
70 , 110 , 350 , 290
These will all have the same absolute values of trig functions. BUT the signs will be different in the different quadrants.
Am I missing something? I think it's a little different because there's a 150 degree angle that starts in quadrant one and goes to quadrant two, called the principal angle, and the left over 30 degree angle made by the original 150 degree angle is the related acute angle. And it's saying that the ratios for the related acute angle will be equal (save for the signs) to the principal angle.
So I guess using the 110 degree example from earlier, my notes are essentially saying that the 70 degree angle (the related acute angle) created by the space between the x axis and the original 110 degree angle has equal (except the signs) primary trig ratios to the oringial (principal angle) 110 degrees?
How does this work? Is it just what you've been explaining to me but applied slightly differently? I can't figure out what I seem to be missing, I think there's something obvious /:
The trig functions are ratios of x, y and the hypotenuse sqrt (x^2+y^2).
Therefore if you take the angle between the ray and the x axis you can figure out the sin, cos and tan. The ratios are the same in every quadrant but the signs are not.
They are also the same using (90-the angle to the x axis) which is the complement. When sketching I do not differentiate between drawing 70 degrees from x and 20 degrees from y.
In the end
sin = y/sqrt(x^2+y^2)
cos = x/sqrt(x^2+y^2)
tan = y/x
Thank you! You've been an immense help
Use the rated acute angle to state an equivalent expression
sin 290
plzz help answer this I'm confused