Does anyone have an idea on how to memorize exact values?

Question

I have to memorize all the exact values for sin, cos, and tan. There's like 51 different numbers. Should I just go like one at a time and use flash cards or is there a better way?

Answer 1

All you really need to do is memorize sin and cos in the 1'st quadrant:
sin(0) = cos(π/2) = (1/2)√0
sin(π/6) = cos(π/3) = (1/2)√1
sin(π/4) = cos(π/4) = (1/2)√2
sin(π/3) = cos(π/6) = (1/2)√3
sin(π/2) = cos(0) = (1/2)√4

Notice how it goes √0, √1, √2, √3, √4 ? That's easy (and that's why we write √0 instead of 0 and √1 instead of 1)

Then you need to remember how both functions 'act' in each quadrant as the angle increases. Sin goes from 0 to +1 in the 1'st quadrant, +1 to 0 in the 2'nd quadrant, 0 to -1 in the 3'rd quadrant, and -1 to 0 in the 4'th quadrant. Cos goes from +1 to 0 in the 1'st quadrant, 0 to -1 in the 2'nd quadrant, -1 to 0 in the 3'rd quadrant, and 0 to +1 in the 4'th quadrant.

Then all you have to remember is that
tan = sin/cos
cot = cos/sin
sec = 1/cos
csc = 1/sin
and you're home free.


Doug

Answer 2

ARE YOU CRAZY????

If you paid ANY attention in class, you should be able to generate any such thing on demand.

Here is what I remember about trigonometry on top of my head right now, and I can assure you that I can generate your entire trignometry textbook. Granted they take some experience but nontheless it can still be done.

1.The pythagorean theorem

2.sin^2(x)+cos^2(x)=1

3.e^(ix)=cos(x)+i*sin(x) - Euler's Formula - by far the single most handy thing I know

4.The coordinates on the unit circle are always (cosx, sinx).

5.Lengths of the sides opposite an angle are proportional to the measure of the angle in a triangle. In other words, smaller angles get the smaller sides and bigger angles get the larger side.

Notice, that I don't even know the special triangles like 45-45-90 or the 30-60-90 triangles. I can use 4 and 5 to do that. I can also prove any identity or solve any trig equation using 1 and 2. Number 3 I can use to derive ALL half-angles, double-angle, summation, and difference formulas.

Answer 3

Human memory is associative and emotionally linked. Most "instant memory" gurus use the simple trick of assocaiting the value to be memorized with somthing outrageous. For example to remember Mr, Bulbas name think of him having a "bulbas nose"

Since there are many more than 51 values, I suspect that you are requested to come up with trig values for only special angles such as PI/2 PI/4 etc. Those you should be able to generate on demand if you have paid attention in class.

Answer 4

what you need to do is be able to draw a triangle to the specs of the question.....
the 30:60:90 triangle has sides of 1 root3 and 2 so the tan of 60 is (root3 / 1 opp/adj) and so on ....
the other triangle is 45:45:90 (sides of 1 1 root2)

so ... if the sin is .30, then the ratio of opposite to hypotenuse is .30 to 1 .... (.30)^2 + (B)^2 = 1^2 .09 + (.91) = 1 B= .9539 ....... so the angle was 17.46degrees so,,,,,,,, the cos of that same angle is .9539 / 1

Protagoras works

Answer 5

Actually, there is nowhere near that much to memorize if you understand the relationships among sine, cosine, tangent and cotangent. I know, because I didn't get it the first time I took trigonometry, so I got through by madly memorizing things I was embarassed to discover later I didn't need to memorize at all!

Answer 6

I have to write everything like 20 times each then I use flash cards always works using repetition

Answer 7

Memorize seven a day and you'll have them memorized in about 8 days. That's how I learned Russian.

Answer 8

That is strage because when I went through that, we had a sheet with all the exact values. You shouldn't have to memorize it, ask your prof / teacher if you are allowed to use a reference sheet.

Answer 9

There are only 2 non-trivial triangles you should be expected to remember

(45,45.90) and (60,30,90) you essentially have to remember 4 values... and the definitions and pythagorean... how hard is that?

Answer 10

Try studying while listening to classical music. Your brain remembers the math and links it with the music.