Trigonometry (Module 13)

Exact Trig Values, Trig graphs + how to transform them, rules

pythagoras’ theoreom

a²+ b²= c² (hypotenuse)

sine

sin(degrees) = opp / hyp

• opp = the side opposite to the unknown angle

cosine

cos(degrees) = adj / hyp

• adj= side next to the unknown angle

tangent

tan(degrees) = opp / adj

sin/cos/tan ^-1

uses the ratio to find the angle

• sin(degrees) uses degree to find ratio

exact trig value song

sin(90)

1

cos(90)

0

sine curve values

Sine Value	Angles (Degrees)
1	90°
0	0°, 180°, 360°
-1	270°

cosine curve values

Cosine Value	Angles (Degrees)
1	0°, 360°
0	90°, 270°
-1	180°

finding sin graph value in terms of degrees

1. find y value and connect with point it meets the curve to x-axis

2. works the other way around too

tan graph + finding next equal point

repeats in “periods” of 180°

• to find next equal point add angle by 180°

• 0 = 180, 1 = 45, -1 = 135

sine rule (to find sides)

sine rule (to find angles)

B = sin^-1 ( [ b * sin(A) ] / a )

cosine rule

cosine rule (rearranged for angle)

area of a triangle using sine

f(x) ± d

vertical translation

• (+) = up // (-) = down

f(x ± d)

horizontal translation

• (+) = left / (-) = right

-f(x)

reflect over x axis

f(-x)

reflect over y axis

af (x)

vertical

• IF a > 1, stretch

• IF a < 1, compress

f (ax)

horizontal

• IF a > 1, compress

• IF a < 1, stretch