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What's the fastest and most efficient way to learn the unit circle? Failed Trig because I didnt bother to memorize it all. Figured if I sat down and did whatever the best method was, I could get it like I did with my times tables.
1) Memorize the graphs. Sin(x) is an odd function which crosses the origin. Cos(x) is an even function, et cetera. Also, sin(n*x) and cos(n*x) are both periodic with a period of 2pi/n.
2) Okay, let's talk about the angles of 30, 45, 60, and 90 degrees.
sin 30 = 1/2 (the square root of 1 divided by 2)
sin 45 = sqrt 2 / 2 (notice: the square root of 2 > the square root of 1)
sin 60 = sqrt 3 / 2 (notice: the square root of 3 > the square root of 2)
sin 90 = 1 = sqrt 4 /2 (notice: the square root of 4 > the square root of 3)
Do you see what's going on here? The sin function is increasing from 0 to 90 degrees, so we know to go from 1/2 to sqrt2/2 to sqrt3/3, etc. Then it decreases from 90 to 180 degrees. (You also need to know your quadrants to tell if it's positive or negative)
Cos(x) is basically the same thing, but it's DECREASING from 0 to 90 degrees, and then it becomes negative. In other words, cos(x) = sin (x+90 degrees)
cos (30 degrees) = sqrt 3/2
cos (45 degrees) = sqrt 2/2
Blah blah blah. It should seem pretty simple now, just practice.
>>8083938
**correction: sin(x) actually decreases from 90 degrees to 270 degrees, and cos(x) is decreasing from 0 degrees to 180 degrees.
>>8083938
Ok thanks.
Got any youtube video suggestions to supplement this advice
>>8083919
Just think of it as a cartesian plane with 4 total possible x or y values.
>>8083919
The unit circle should be intuitive
You should stop doing maths now
https://phet.colorado.edu/sims/html/trig-tour/latest/trig-tour_en.html
There you absolute faggot.
>>8083919
In the first quadrant, as the angle grows,
the x-coordinate changes
[math] \displaystyle
\frac{\sqrt{4} } {2} \rightarrow \frac{ \sqrt{3} } {2} \rightarrow \frac{ \sqrt{2} } {2} \rightarrow \frac{ \sqrt{1} } {2} \rightarrow \frac{ \sqrt{0} } {2}
[/math]
The y-coordinate changes in the opposite direction.
In the other quadrants the only change is the sign of x and y
idk
in my trig class we got a little chart with the unit circle and some formulas on it we could use on tests and stuff
Is this not normal? I don't really get how memorizing a specific formula determines how good or bad at math I am.
My friend has this nifty chart, although I memorized mine through just grinding a schaum's book of trig and just doing a lot of pre calc hw. I personally don't use this but this helps him a lot
>>8085779
For my class we were just given the identities
>>8085794
It had that too. It had trig identites, the unit circle, various other forumals. It was pretty handy.
I'm scared about doing other math that I won't have something like that.
What I do worst is memorizing formulas. If I grind something a lot I'll remember the formula but I usually don't do a specific type of problem over and over and over again enough to memorize it.
By now it's intuitive, but when I occasionally forget, I use this.
If you know your trig identities the only values you need to memorize are sin30deg, cos30deg, sin45deg, cos45deg. From those you can get all the other common unit circle values.
>>8083919
Switch to rational trig and never memorize a trig identity again.
>>8083919
You have to learn your 30-60-90 and 45-45-90 triangles. Memorization is definitely not the way to go.
>>8083938
Wtf man do you even know trigo basics....
Sin(x) decreases till 45° and increases from 45°-225° and cos(x) increases till 45° and decreases from 45°-225° and then again increases from 225°-360°. This was the first thing that my teachers taught me in first trigo lecture.... pls don't answer incorrectly in here if you don't know enough.
>>8085779
Lol trigo is all about identities an you have to memorize and understand them all in order to master it. No on is going to give you charts and identities written on it in exam or when you need to use them. I learnt like 60 trigo identities in high school and I remember them pretty well till now.
