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PPT – Trigonometry PowerPoint presentation | free to download - id: 41f3ef-YWM3N

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Trigonometry

?

Definition of an angle

Terminal Ray

Counter clockwise

Initial Ray

- clockwise

Terminal Ray

Coterminal angles angles with a common terminal

ray

Terminal Ray

Initial Ray

Coterminal angles angles with a common terminal

ray

Terminal Ray

Initial Ray

Radian Measure

Definition of Radians

C 2pr

C 2p radii

C 2p radians

360o 2p radians

r

180o p radians

1 Radian ? 57.3 o

r

Unit Circle Radian Measure

Unit Circle Radian Measure

Unit Circle Radian Measure

Degrees

Converting Degrees ? Radians

Converts degrees to Radians

Recall

Converts Radians to degrees

more examples

Trigonometric Ratios

Basic ratio definitions

Hypotenuse

Opposite Leg

Reference Angle

?

Adjacent Leg

Circle Trigonometry Definitions

(x, y)

Radius r

Opposite Leg y

Adjacent Leg x

reciprocal functions

Unit - Circle Trigonometry Definitions

(x, y)

Radius 1

Opposite Leg y

Adjacent Leg x

1

Unit Circle Trig Ratios

sin

cos

tan

(, )

(-, )

(, -)

(-, -)

Skip p/4s

Reference Angles

Unit Circle Trig Ratios

sin

cos

tan

(, )

(-, )

(-, -)

(, -)

Unit Circle Trig Ratios

sin

cos

tan

(, )

(-, )

(0 , 1)

Quadrant Angles

(1, 0)

(-1, 0)

sin

cos

tan

0

/2p

1

0

0

0

Ø

1

(0, -1)

(-, -)

(, -)

0

-1

0

Ø

-1

0

View p/4s

Unit Circle Radian Measure

sin

cos

tan

(-, )

(, )

Quadrant Angles

sin

cos

tan

1

0

/2p

1

0

0

0

Ø

1

(-, -)

(, -)

0

-1

0

Ø

Degrees

-1

0

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Graphing Trig Functions

f ( x ) A sin bx

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Amplitude is the height of graph measured from

middle of the wave.

Amplitude

Center of wave

f ( x ) A sin bx

f ( x ) cos x

A ½ , half as tall

f ( x ) sin x

A 2, twice as tall

Period of graph is distance along horizontal axis

for graph to repeat (length of one cycle)

f ( x ) A sin bx

f ( x ) sin x

B ½ , period is 4p

f ( x ) cos x

B 2, period is p

A unit circle is a circle with a radius of 1

unit. For every point P(x, y) on the unit circle,

the value of r is 1. Therefore, for an angle ? in

the standard position

The End

Trigonometry Hipparchus, Menelaus, Ptolemy

Special Right Triangles The Pythagoreans

Graphs Rene DesCartes

Reference Angle Calculation

2nd Quadrant Angles

3rd Quadrant Angles

4th Quadrant Angles

Return

Unit Circle Degree Measure

90

120

60

135

45

150

30

0/360

180

330

210

225

315

300

240

270

Return

Unit Circle Degree Measure

sin

cos

tan

30

90

(-, )

(, )

45

120

60

135

45

60

150

30

Quadrant Angles

0/360

180

sin

cos

tan

1

330

210

0/360

1

0

0

225

315

0

Ø

1

90

300

240

(-, -)

(, -)

0

-1

0

180

270

Ø

Return

-1

0

270

Ex. 4

Ex. 3

Ex. 6

Ex. 5

return

Circle Trigonometry Definitions Reciprocal

Functions

(x, y)

Radius r

Opposite Leg y

Adjacent Leg x

return

Unit Circle Radian Measure

1