Precalculus

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What goes in quadrant 1?

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Chapter 4 review

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1

What goes in quadrant 1?

(+,+) All Pythagorean identities are positive

<p>(+,+)  All Pythagorean identities are positive</p>
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2

What goes in quadrant 2?

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

<p>(-,+) All Pythagorean identities are negative except sin, csc <strong>A</strong></p>
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3

What goes in quadrant 3?

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

<p>(-,-) All Pythagorean identities are negative except tan, cot <strong>T</strong></p>
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4

What goes in quadrant 4?

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

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5

How can I remember where the six functions are positive ?

C (COS, Q4)

A (ALL OF THEM Q1)

S (SIN, Q2)

T (TAN, Q3)

<p><strong>C</strong> (COS, Q4)</p><p><strong>A</strong> (ALL OF THEM Q1)</p><p><strong>S</strong> (SIN, Q2)</p><p><strong>T</strong> (TAN, Q3)</p>
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6

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

<p>0 degrees, 0 radians - 0</p><p>30 degrees, pi/6 radians - 1/2</p><p>45 degrees, pi/4 radians - (sqrt2)/2</p><p>60 degrees, pi/3 radians - (sqrt3/2</p><p>90 degrees, pi/2 radians - 1</p><p>180 degrees, pi radians - 0</p><p>270 degrees, 3pi/2 radians - 1</p>
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7

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

<p>0 degrees, 0 radians - 1</p><p>30 degrees, pi/6 radians - (sqrt3)/2</p><p>45 degrees, pi/4 radians - (sqrt2)/2</p><p>60 degrees, pi/3 radians - 1/2</p><p>90 degrees, pi/2 radians - 0</p><p>180 degrees, pi radians - -1</p><p>270 degrees, 3pi/2 radians - 0</p>
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8

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

<p>0 degrees, 0 radians - 0</p><p>30 degrees, pi/6 radians - (sqrt3)/3</p><p>45 degrees, pi/4 radians - 1</p><p>60 degrees, pi/3 radians - sqrt3</p><p>90 degrees, pi/2 radians - undefined</p><p>180 degrees, pi radians - 0</p><p>270 degrees, 3pi/2 radians - undefined</p>
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9

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, …

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