TRIGONOMETRY: REVIEW

SOHCAHTOA
Show that tanӨ=sin Ө/cosӨ

Pythagoras a2+b2=c2
Show that cos2 Ө+sin2 Ө=1
(÷c & substitute with trig ratios)
H
O
Ө
•
π radians =180°
•
Non-right Angles: When would you use the following?
a
b
c


sin A sin B sin C
A
a  b  c  2bcCosA
2
2
2
1
A  abSinC
2
SOH CAH TOA
Sin=0/H --O=H Sinx
Applet:
http://www.ies.co.jp/math/products/trig/applets/sixtrigfn/sixtrigfn.html
Sketch the 3 trig functions
Sine Graph y=sinx
y
Amplitude:
Period:
Frequency:
1
Amplitude=1
Period=360 or 2π
90
– 1
180
270
360
x
Cosine graph
y
Amplitude:
Period:
Frequency:
1

2
– 1

3
2
2
x
Tangent graph
y
4
Amplitude:
Period:
Frequency:
2

2
– 2
– 4

3
2
2
x
y=±A sinB(x±C) ± D
-sinx

-cosx
-tanx
Reflects in the x axis
1–
6.28318531
1.2
3
2
0.78539816
1.2

 1
22
y
y
1
1
90
– 1
180
270
360

x
2
– 1

3
2
2
x
asinx
acosx
atanx
Changes the amplitude (max distance from
resting) of the graph
 y=2sinx
1
 y= 2 cosx

1–
6.28318531
1.2
3
2
0.78539816
1.2

 1
22
y
y
1
1
90
– 1
180
270
360

x
2
– 1

3
2
2
x
sinbx
cosbx tanbx
Changes the frequency (how often it
repeats in 2π) & period (horizontal
distance for one cycle)
 y=sin3x
frequency x3 , period ÷3
 y=cos1/2 x
frequency ½ ed, period x2

1–
6.28318531
1.2
3
2
0.78539816
1.2

 1
22
y
y
1
1
90
– 1
180
270
360

x
2
– 1

3
2
2
x
sin(x-c) cos(x-c) tan (x-c)
Moves graph sideways ( + left
 y=sin(x-45)
 y=cos(x+90)
- right )

1–
6.28318531
1.2
3
2
0.78539816
1.2

 1
22
y
y
1
1

2
90
180
270
360
x
– 1
– 1

3
2
2
x
sin(x)+d cos(x)+d tan(x)+d
Moves graph up or down (+ up - down )
 y=sin(x)+2
 y=cos(x)-1

1–
6.28318531
1.2
3
2
0.78539816
1.2

 1
22
y
y
1
1
90
– 1
180
270
360

x
2
– 1

3
2
2
x
On Graphics Calculator
eg: sketch f(x)=3sin2(x-π/4)



Make sure you are in the right mode (rad/degrees)
Enter equation (use brackets around inner function)
Adjust view window:
◦ Think about the domain you want to see:
one cycle/ 2π (consider frequency & horizontal shift)
◦ Think about the range (consider amplitude change &
vertical shift)
◦ If in radians, set the step as something including π (often
π /2)

Remember you can g-solve for points/use table
function to plot.