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)

• π radians =180°

• Non-right Angles: When would you use the following?

Ө

O

A

H

C

c

B

b

A

a

sinsinsin bcCosAcba 2222 abSinCA

2

1

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

1.2 – 1.2 1.2 – 1.2 405 – 45 1.2 – 1.2

x

90

90

180

180

270

270

360

360

y

– 1

– 1

1

1

Amplitude=1Period=360 or 2π

Amplitude:Period:Frequency:

Cosine graph

1.2 – 1.2 1.2 – 1.2 6.28318531 – 0.78539816 1.2 – 1.2

x

2

2

32

32

2

2

y

– 1

– 1

1

1 Amplitude:Period:Frequency:

Tangent graph

4 – 4 4 – 4 6.28318531 – 0.78539816 4 – 4

x

2

2

32

32

2

2

y

– 4

– 4

– 2

– 2

2

2

4

4 Amplitude:Period:Frequency:

y=±A sinB(x±C) ± D

Reflects in the x axis

-sinx -cosx -tanx

1.2 – 1.2 1.2 – 1.2 405 – 45 1.2 – 1.2

x

90

90

180

180

270

270

360

360

y

– 1

– 1

1

1

1.2 – 1.2 1.2 – 1.2 6.28318531 – 0.78539816 1.2 – 1.2

x

2

2

32

32

2

2

y

– 1

– 1

1

1

asinx acosx atanxChanges the amplitude (max

distance from resting) of the graph

y=2sinx y= cosx

2

1

1.2 – 1.2 1.2 – 1.2 405 – 45 1.2 – 1.2

x

90

90

180

180

270

270

360

360

y

– 1

– 1

1

1

1.2 – 1.2 1.2 – 1.2 6.28318531 – 0.78539816 1.2 – 1.2

x

2

2

32

32

2

2

y

– 1

– 1

1

1

sinbx cosbx tanbxChanges 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

1.2 – 1.2 1.2 – 1.2 405 – 45 1.2 – 1.2

x

90

90

180

180

270

270

360

360

y

– 1

– 1

1

1

1.2 – 1.2 1.2 – 1.2 6.28318531 – 0.78539816 1.2 – 1.2

x

2

2

32

32

2

2

y

– 1

– 1

1

1

sin(x-c) cos(x-c) tan (x-c) Moves graph sideways ( + left

- right ) y=sin(x-45)y=cos(x+90)

1.2 – 1.2 1.2 – 1.2 405 – 45 1.2 – 1.2

x

90

90

180

180

270

270

360

360

y

– 1

– 1

1

1

1.2 – 1.2 1.2 – 1.2 6.28318531 – 0.78539816 1.2 – 1.2

x

2

2

32

32

2

2

y

– 1

– 1

1

1

sin(x)+d cos(x)+d tan(x)+dMoves graph up or down (+ up -

down )y=sin(x)+2y=cos(x)-1

1.2 – 1.2 1.2 – 1.2 405 – 45 1.2 – 1.2

x

90

90

180

180

270

270

360

360

y

– 1

– 1

1

1

1.2 – 1.2 1.2 – 1.2 6.28318531 – 0.78539816 1.2 – 1.2

x

2

2

32

32

2

2

y

– 1

– 1

1

1

On Graphics Calculatoreg: 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.