Math is a wonderful thing

i need you to edit in pi symbols, degrees, fractions and the like because I don't know how.

Trigonometry 1

Radians & Degrees

Definition of a radian:
- One radian is the angle at the centre of a circle when the arc length is equal to the radius.

- To convert radians into degrees we use the conversion of:
180(degrees) = (pi) radians.

This conversion comes from our knowledge that the angle of the centre of a circle is 360(degrees). If the circle has radius R, then the arc length, S, is the full circumference, which is 2(pi)r.

Therefore 2(pi)radians = 360(degrees) so (pi)radian = 180

Simple Conversions:(Do these as a type of question, i.e. if I have 60 degrees, how many radians do I have. so have the degrees come up first and then the radians in transition, if you know what i mean)

90(degrees) = (pi over 2)
60(degrees) = (pi over 3)
270(degrees) = (3pi over 2)

Complex Conversions:

These conversions do not appear in the log tables and thus you must calculate them yourself.

To do this you have to:(can i get a picture of each step on the side? i.e. for step 2 can I have something that shows what it actually looks like?

- Use your conversion of 180(degrees) = (pi) radian
- Find one degree by putting (pi) radian over 180(degrees)
- If 1(degree) =(pi)radian over 180(degrees) then X(degree) = X(pi)radians over 180(degrees) where X is the number of degrees you look to convert.

Conversion Example:
150(degrees) =150(pi) over 180(degrees) = 5(pi) over 6

Converting Radians to Degrees:
- Use your conversion to find (pi)radian and solve for question e.g. (just an example, not a question i will ask class)

Convert 5(pi) over 3 to degrees.
(pi) = 180(degrees)
5(180degrees) over 3 = 300(degrees)

ARC FORMULA:

s = r(theta)
where S is the arc length, R is the radius and (theta) is the angle
(theta) must be in radians.

We can use this formula if we only need to find one unknown.

Example:

Find the arc length of a circle with radius 3cm and an angle of 45(degrees)

First we must convert 45(degrees) into (pi) over 4 radians
Then we use the formula to find the arc length
s = r(theta)
s = 3(pi) over 4

Trigonometric Ratios:



SOHCAHTOA

sin(theta) = opposite(over)hypotenuse = A(over)C
cos(theta) = adjacent(over)hypotenuse = B(over)C
tan(theta) = opposite(over)adjacent = A(over)B

Other trigonometric ratios are:

sec(theta) = 1(over)cosA
cosec(theta) = 1(over)sinA
cot(theta) = 1(over)tanA = cosA (over) sinA

COMPLEMENTARY ANGLE RESULTS(cant find picture like one in book)

All the angles in a triangle must be equal to 180(degrees)

Therefore if a right angled triangle has an angle A, the final angle can be calculated as 90(degrees) - A.

Cos(90degrees - A) = sinA
Sin(90degrees - A) = cosA
Tan(90degrees - A) = cotA







I cant do the last page of section 2. God, Kate, I'm sorry this is so crap =( I'm useless at stuff like this. I realise i've left you with a lot of work to do, again, I'm really really sorry