SL Topic 3.1 & 3.2 Revision Notes

Topics 3.1 & 3.2 Revision Notes

Trigonometry

IB Math SL


Trigonometry

IB Math SL

Right-angled triangles

It’s important that for all degree measurement you w rite the degree symbol.

Pythagoras’ Theorem You need to be able to calculate missing sides in right ang led triangles, given two sides by using Pythagoras’ theorem. c2 = a2 + b2

The angles that are multiples of π are radians. But not all radian measures are multiples of π. For example, an angle that is 3 radians is a little less than π radians. π radians, by the way, can also be expressed as 3.14 radians.

b

*For trigonometry you need to pay attention to the MODE of your calculator.

c

To convert radians to degrees multiply by



To convert degrees to radians multiply by

180  

180

r

A rule of thumb is π = 180°. Be careful when you are using your calculator to find angles from the unit circle. The calculator will give you one answer, usually between 0º and 90º, but there will be two answers between 0º and 360º.

a

SOHCAHTOA If you need to find missing angles and missing sides in right triangles use SOHCAHTOA (Sin Opposite Hypotenuse, Cosine Adjacent Hypotenuse, Tangent Opposite Adjacent)

e t i s o p p o



sin  hypotenuse



Sine, Cosine and Tangent. The coordinates that are labeled on the Unit Circle above are the sine and cosine values of each of those angles. You might find it useful to memorize the entire Unit Circle, which actually isn’t as daunting as it may seem because if you know one quadrant, then you can figure out the other three.

opposite

hypotenuse adjacent cos  hypotenuse opposite tan  adjacent

The first coordinate is the cosine of the angle and the second coordinate is the sine of the angle. For example,

3  5  1  5    and sin    2  3  2  3 



θ

adjacent

cos



To find the tangent of any of those angles you can use the identity: tan  

Being familiar with the Unit Circle will help you figure out the sine, cosine and tangent of any angle between 0 and 2π. Typically IB will will only expect you to know the sine, sine, cosine and tangent of , π,

, and 2π.

sin  cos 

.

Another identity that you need to be familiar with is known as the 2 2 Pythagorean Identity: Identity: sin θ + cos θ = 1 Note: If the question wants the exact number it must be given as a fraction. 2

2

2

Remember: sin θ = (sin θ) ≠ sin(θ) .

1

2


Trigonometry

IB Math SL

Two other formulae that you need to be familiar with are AREA OF A SECTOR and ARC LENGTH. A sector is like a slice of pizza. An arc is a section of the circumference, or the crust of that slice of pizza. Arc length = r θ, where θ is the angle measured in radians, r is the radius. Area of a sector =

1 2

r 2 , where θ is the angle measured in radians, r is the radius.

EXAMPLE In the circle below the radius is 12cm and the angle of the minor sector at the center of the circle is 2.51 radians.

a) Find the minor arc length b) Find the area of the major sector (the unshaded region) ANSWERS

3

SL Topic 3.1 & 3.2 Revision Notes

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