Precalculus

Chapter 4 review

What goes in quadrant 1?

(+,+) All Pythagorean identities are positive

What goes in quadrant 2?

(-,+) All Pythagorean identities are negative except sin, csc A

What goes in quadrant 3?

(-,-) All Pythagorean identities are negative except tan, cot T

What goes in quadrant 4?

(+,-)All Pythagorean identities are negative except cos, sec C

How can I remember where the six functions are positive ?

C (COS, Q4)

A (ALL OF THEM Q1)

S (SIN, Q2)

T (TAN, Q3)

TRIGONOMETRIC FUNCTIONS OF ANY ANGLE : SIN

0 degrees, 0 radians - 0

30 degrees, pi/6 radians - 1/2

45 degrees, pi/4 radians - (sqrt2)/2

60 degrees, pi/3 radians - (sqrt3/2

90 degrees, pi/2 radians - 1

180 degrees, pi radians - 0

270 degrees, 3pi/2 radians - 1

TRIGONOMETRIC FUNCTIONS OF ANY ANGLE : COS

0 degrees, 0 radians - 1

30 degrees, pi/6 radians - (sqrt3)/2

45 degrees, pi/4 radians - (sqrt2)/2

60 degrees, pi/3 radians - 1/2

90 degrees, pi/2 radians - 0

180 degrees, pi radians - -1

270 degrees, 3pi/2 radians - 0

TRIGONOMETRIC FUNCTIONS OF ANY ANGLE : TAN

0 degrees, 0 radians - 0

30 degrees, pi/6 radians - (sqrt3)/3

45 degrees, pi/4 radians - 1

60 degrees, pi/3 radians - sqrt3

90 degrees, pi/2 radians - undefined

180 degrees, pi radians - 0

270 degrees, 3pi/2 radians - undefined

Characteristics of y=sinx and y=cosx

domain: all real numbers

range: -1 <= y <= 1

amplitude: half the difference of the maximum M and minimum m values : a=1/2 (M-m)

periodic: repeating pattern-cycle,

y=sinx : 0, pi, 2pi, 3pi, 4pi …

y=cosx : 0, pi/2, 3pi/2, 5pi/2, 7pi/2, 9pi/2, …