Trig help! I'm taking Cal2, but I never had trig. Can somebody explain the basic pi circle to me?

Question

I understand the Calculus concepts, but the trig trips me up, esp. the sin, cos, etc. I've seen some sort of circle that uses pi and the square root of 2, but I don't have a copy, and I don't know what it means. Can anybody point me in the right direction? My hs didn't offer trig, and now I'm in college, and I'm having to play catch-up. Thanks in advance!

Answer 1

It would be very difficult to explain all you need to know for Calc 2. The best thing to do is hire a tutor for a couple of weeks to go over the basics of trig with you and how the concepts apply to calculus.

Answer 2

So you want us to teach you trig, eh? It's ok, and feel free to ask me and email me...

degrees and π

There are different ways to express angles

The most common type of expressing angles is degrees. A degree is a measure of the angle formed by cutting a circle into 360 equal "pies". Thus, 360º = 1 whole circle.

Another useful expression is using radians. A radian is defined as the measure of the angle that intercepts the circle on an arc that measures the same as the radius of the circle. That is, if you start from a point A of a circle with center O, go through the circumference of the circle with a distance of r (radius), assign that point as B, then angle AOB = 1 radian.
Since C = 2πr, C/r = 2π. Therefore dividing the whole circle into r equal parts is equal to 2π. Thus, 2π radians = 1 whole circle.

Since
360º = 1 whole circle
2π radians = 1 whole circle, therefore
2π radians = 360º
π radians = 180º

Trig in calculus often use radians instead of degrees, so it's better that you know how to deal with radians.

If you're still having difficulty with radians,.try to convert it first into degrees using the conversion factor (π radians/180º) or its reciprocal.

E.g.
5π/6 radians = 5π/6 radians (180º/π radians) = 150º
Don't forget to convert it into radians again for final answers.

Trig functions (sin,cos,etc.)

The six trig functions are used in calculus,
sin = sine
cos = cosine
tan = tangent
csc = cosecant
sec = secant
cot = cotangent

Let us start:
To get an introduction with them, take a right triangle first:
rt. triangle ABC, with C = right angle. Name the side opp. A side a, the side opp. B side b, and the side opp. C side c.

Thus, by the pythagorean theorem,
c² = a² + b²

The 6 trig functions are defined as
sin = opposite side/hypotenuse = opp/hyp = O/H
cos = adjacent side/hypotenuse = adj/hyp = A/H
tan = opposite side/adjacent side = opp/adj = O/A
csc = H/O
sec = H/A
cot = A/O

That is:
sin A = a/c
cos A = b/c
tan A = a/b
csc A = c/a
sec A = c/b
cot A = b/a
sin B = b/c
cos B = a/c
tan B = b/a
csc B = c/b
sec B = c/a
cot B = a/b

You notice that
sin A = cos B
tan A = cot B
csc A = sec B
Since A + B = 90º, then B = 90º - A, and
sin A = cos (90º - A)
tan A = cot (90º - A)
csc A = sec (90º - A)

the co- means "cofunction". i.e. sine and co-sine are cofunctions, etc.

You also notice that
sin x = 1/csc x
cos x = 1/sec x
tan x = 1/cot x

Thus you only need to remember sin cos and tan, because the other three are just reciprocals of these three.

At this point it is very hard for me to teach you how to visualize sin cos and tan. If you'll let me contact you I will give some explanations.

Feel free to contact me!

kevin!
^_^

Answer 3

Hi. Pi is the number used to describe the relationship between a circle and it's diameter. But it has a close relationship to many other things. You'll need to read up, I'm afraid. The simplest relationship is that a circle's circumference is pi times the diameter. With a circle of 1" diameter the circumference is 3.1415926535... Most folks just round off to 3.1416.

Answer 4

The circumference of a circle is the diameter times pi.

C = π x d

The area of a circle is the radius of the circle times the radius of the circle times pi.

A = π x r x r

Answer 5

Pi is a number which is 3.14159265359 it never finishes (and by the way i knew that number off the top of my head)
you get pi by dividing the circumference of a circle by its diameter

Answer 6

i think by "pi circle" you mean UNIT CIRCLE.

try a google search for unit circle, should help a little

Answer 7

mmmm... pi *drool*