Planr requires assistance with Trigonometry!

[Planr]

I'm having trouble with this online Algebra 2 credit recovery course i'm doing. The lessons tutorials are crap and are usually unrelated to the material on the mastery tests. Instead of being straightforward with us in the tutorial and showing us what to do, the tutorial instead drones in an endless "wopwopwop" of philosophical questioning like "suppose..." or "but what if...?". It's infuriating, and I've had to learn all the material myself on third-party sites like mathisfun and khanacademy.

One question i'm having particular trouble with is "what is the range of y=sinθ?"
The tutorial didn't address this at all or explain how to find the ranges of angles on a unit circle, so i'm in the dark on this. Anyone able to help me out?

[Ad Bot]

[XR-7]

By the way it appears, it should be [0, ∞). After all, the positive sine ratio would have to be above the x-axis. If it is simply confined to the unit circle though, its highest value would have to be 1 (since r=1). I'm not totally confident on whether that's what the question specifies or not.

[Ipquarx]

The sine and cosine functions are really just the X and Y coordinates on the unit circle, so the range (y coordinates) can only be in the range [-1, 1].

explained in the form of a gif:

[Oasis]

You're going to have a bunch of fun in Calc. :)

[Ladios]

Its not until calc 3 that you really appreciate trig.
It feels like they teach math out of order. *shrugs*

Jeeze and if you learned derivtives before physics wow things would seem so easier
Then you wouldnt see all the equations as just arbitrary functions but as sensible integrations of functions of velocity or whathaveyou.

[Blockzillahead]

ummmmmmmmmmmmmmmmmmmmmmm quick brain pull up old trigonometry memory!

2PI is the range I think
or 360 degrees

oh nvm im thinking about cycle

domain is for x. so (XER)
range is for y. it never goes above 1 or below -1
(y | yER, -1 <= y <= 1)

[Clix]

Someone needs to make a homework help mega thread.

[Kearn]

domain is negative infinity to infinity, range is -1 to 1

[SeventhSandwich]

One question i'm having particular trouble with is "what is the range of y=sinθ?"
The tutorial didn't address this at all or explain how to find the ranges of angles on a unit circle, so i'm in the dark on this. Anyone able to help me out?

A unit circle is by definition a circle with a radius of 1. What that means is that because the coordinates (x,y) on a unit circle are equal to (cos,sin), sin(x) only gives numbers from -1 to 1.

So the range is [-1, 1].

If you don't understand how an angle translates into a trigonometric ratio, look at this chart for awhile until it makes sense.

[Axo-Tak]

Basically, you can use this acronym, SOHCAHTOA, to know which ratios to use. Think logically afterwards. For example, the tangent of an angle at 90 would not compute because you're implying the triangle is an open square.

Sine:
Opposite of the angle (like on the other side of the triangle)
Hypotenuse
Cosine:
Adjacent to the angle
Hypotenuse
Tangent: (this is really important)
Opposite
Adjacent

Paper and pencil can help. For example, it (and geometric proofs) helped me with the Blob Terrain Generator.