Question

Trig Values In All 4 Quadrants Worksheet, Help Please

Answer 1

Now we're working with the unit circle and trying to remember our values for various radian/degree measures. Have you been introduced to radians at all yet?

Answer 2

Yes a little bit

Answer 3

Yeah, because personally I am not really remembering these in terms of degrees, just radians. But okay, so we have our "nice" trig values to come out as:
Quadrant 1: 30, 45, 60
90 in between
Quadrant 2: 120, 135, 150
180 in between
Quarant 3: 210, 225, 240
270 in between
Quadrant 4: 300, 315, 330
End at 360 (same as 0). So the first problem is one of those clean numbers (would be kind of mean if it wasnt). Now it's just a sort of memorization of values at all of those clean numbers. Me personally, I like to start at 60 degrees (π/3) and then work my away around in whatever direction I need to go. I start at 60 because I know cos60 is going to give me 1/2, which is a nice number. Hmm.....I almost would want to draw it to be honest. Might be hard to fit, but I like the visual better, because there is a pattern to knowing these values that is good to know, so hang on.

Answer 4

Now that can give me a start to explaining the pattern. Starting from 60 degrees and ticking down, cosine goes √1, √2, √3, 1, √3, √2, √1, 0. With 2 always on the bottom EXCEPT when I get to a value of 1. The sin value at those points is going to be flipped. So instead of 1 and going up, I start from 3 and go down.
√3, √2, √１, 0, -√1, -√2, -√3, -1. The reason sin became negative there is because Im ticking down from 1st to 4th quadrant, so sin (or the y-value) is supposed to be negative there. So really, you could go around the whole circle just going √1, √2, √3, 1, √3, √2, √1, 0, √1, √2, √3, 1, √3, √2, √1, 0, √1, √2, √3, 1, etc, etc, just making sure to get the correct sign based ont he quadrant youre in. So yeah, now to the 1st problem. It wants cosine at 315. So I kinda drew it in the picture, but if I start at the number I like of 60 (or you can start at 0 if it works better for you since cos there is 1), then I count down √1, √2, √3, 1, √3, √2. So Ive ticked down to √2 (remember, all of these values are over 2), and in this quadrant, cosine is positive, so my answer is √2/2. Again, lot of memorization to it, but there are tricks for it, this is just how I go about remembering.