Using the special triangles from Lesson 5.2, sketch two angles in the Cartesian plane that have

Hi emilyliv

Sorry for the late reply, didn't have an opportunity till now to respond.

Anyway, here's a look at what all three functions look like on a cartesian plane -- just as a visual:


We do notice that all three trigonometric functions intersect at some point, but they're never all the same.

Using special triangles, we can see that sine and cosine express the same ratio several times:



Sin(45) = cos(45)
Sin(60) = cos(30)
Sin(30) = cos(60)

It's hard to tell from the special triangles when sine and tangent are the same, so the knowing how they look like graphed helps.

Sin(0) = Tan(0)

Hope this helps

So for sine can you use any special triangle since sine and cosine express the same ratio several times?
this was the answer for sine

Can't recall the question:


Remember what I taught about the CAST rule, all trig. functions are positive in quadrant 1, and only sine is positive in quadrant 2.

By orienting the special triangle about the x-axis in quadrant 2, you see this clearly.



The way this question is worded is awkward, almost hard to understand. I won't dwell on it too much

Okay so just to clarify, for example, cosine, it is only positive in quadrants 1 and 4, so cos(60 in quadrant 1 because 90-30 = 60,  which equals to cos(60 = 1/2 and than orientates to quadrant 4 which is 360 - 60 = 300,  which equals to cos(300 = 1/2 and in this case we would use this following special triangle?

Look at the special triangle in the first quadrant above.

If we use 45 as a reference angle, and use cosine, we get 1/√2

If we put that special triangle in the 4th quadrant, and use 45 as a reference angle, you will get 1/√2 again. Except if the special triangle is in the 4th quadrant, it's actually 360 - 45 = 315.

Therefore, cos(45) and cos(315) are the same.

This logic can be applied to the 30,60,90 triangle as well.

For example, taking cos(60) in the first quadrant, we get the ratio 1/2. In the fourth, we have cos(300) also gives 1/2. So cosine(300) = cosine(60). In addition, cos(30) = √3/2, so does cos(330) = √3/2

Thanks that helped, I was just getting confused which special triangle to use, in this case, I used the 60-degree special triangle.

if u need more clarification, msg back 👍

TY :)

TY :)