Secular Elation

Sorry, just had to vent.

Friar Bellows

Don't worry, you're not alone. Students have been venting over geometry for thousands of years.

echidna

Please Lord, just send me a sine.

fando

Is that euclidean geometry? Man, if only grad-level science courses were that easy.

Hang in there.

Secular Elation

No, not geometry. I am taking plane trigonometry--namely, college trigonometry. Regular geometry is easy (areas and volumes of regular shapes, etc.) but what we're doing in this class is taking me much time to study.

What particularly makes it difficult for me is that we must work with both degrees and radians. Converting between them is easy, but when we apply the concepts to a coordinate plane and find what are called 'reference angles' as well as finding, say, the exact value of "cos 405'". All without calculator.

LeftCoast

Ah yes, reference Angles. Learn them, love them, use them. If you go on to take physics, these'll come in real handy. Just wait'll you hit second semester calculus and have to memorize all of the trigonometric substitutions for computing definite and indefinite integrals.

Principia

Here's a way to remember them:

deg..sin..cos
0.....0....4
30....1....3
45....2....2
60....3....1
90....4....0

For each angle, take the value in the table divide by 4 and take the square root. So for instance, sin 45 = sqrt(2/4) = sqrt(1/2).

Here are some other tips:

Always use the unit circle to figure out the signs. Draw it, and use your finger to go around the circle if you have to.

Always remember that any multiple of 360 added to an angle makes no difference to the sin or cos of that angle.

Always remember that 180 added to an angle changes the sign of sin or cos of that angle.

Always remember that 90 added to an angle changes the sin of that angle to a cos and vice-versa (but the tricky point is that there are also sign changes. So use the unit circle!)

Always remember that all of the other trig functions can be reduced to sin and cos.

Always remember that you will have more to remember.

[ June 14, 2002: Message edited by: Scientiae[retired] ]</p>

Coragyps

And most importantly, always remember to never, never, never get mixed up with spherical trigonometry.

Undercurrent

The mnemonic I always used to tell my kiddies is to memeorize the triangles with sides 1,1,sqrt(2) and 1,2,sqrt(3). The former has angles of 90,45,45, and the latter has angles of 90,30,60. If you just have those two triangles memorized, you can read the trigonometric functions at 30,45, and 60 off them.

The other useful rule was the CAST rule. Basically, you divide the plane up into quadrants with letters in them like this:

[code]
|
S | A
-----------
T | C
|
</pre>[/quote]

The letter stands for which trig ratios are positive for angles in each quadrant (with the first leg on the positive x-axis.) C = cos, A = all, S = sin, T = tan.

The method was to use the standard triangles to compute the ratios in the first quadrant, and the CAST rule to extend to all four quandrants.

m.

nogods4me

if you think plane trig is hard, wait until you get to helicopter trig!