January 19th in your BOOK, 4.2

copyright2009merrydavidson

Special Right Triangles

S O H C A H T O A

opp

adj

opp

hyp

adj

hyp

hyp

opp

hyp

adj

adj

opp

S O H C A H T O A

y

x

rReciprocal functionsParent functions

Reciprocal Identities

Memorize these 11 identities

for a quiz SOON!!!

Look at your unit circle now…

cosine

sine

Check out the Pythagorean Identities

Evaluating Trig Functions:

1: Find the six trig. values for 300.

sin 300o = csc 300o =

cos 300o = sec 300o =

tan 300o = cot 300o =

2 3

3

1

2

3

2

3

33

2

Use your Plate, find the angle, evaluate.

Rationalize the denominator as needed.

Evaluating Trig Functions:

2: Find the six trig. values for -5/4.

sin = csc =

cos = sec =

tan = cot =

2 22

2

2

2

2

2

11

Use your Plate, find the angle, evaluate.

Rationalize the denominator as needed.

2 22

2

5

4

5

4

5

4

5

4

5

4

5

4

Find the sine of the angles listed.30o = 390o = -330o =

1

2

1

21

2What is the NAME of the type of these 3 angles?

What conclusion can you make?

Co-terminal angles have the same trig values.

It takes 360o to get to the same trig value, thus the PERIOD for the sine and cosecant function is 360o

co-terminal angles

2 radians

Find the cosine of the angles listed.60o = 420o = -300o =

1

2

1

21

2

It takes 360o to get to the same place, thus the PERIOD for the cosine and secant function is 360o

or .2 radians

Find the tangent of the angles listed.45o = 225o = -135o = 1 1 1It takes 180o to get the same trig value, thus the PERIOD for the tangent and cotangent function is 180o . radians

Summary of Period

sin/csc/cos/sec have a period of 360o

.

tan/cot have a period of 1800 .

BE CAREFUL TO NOT USE CAPITAL LETTERS. WE WILL LEARN THAT LATER

2 radians

radians

y = sin x

Is this an even or odd function?

y = csc x is also odd.

y = cos x

Is this an even or odd function?

y = sec x is also even

-360 -270 -180 -90 0 90 180 270 360

y = tan x

Is this an even or odd function?

y = cot x is also odd

Now look at the even/odd Identities

What does this mean????

Trig Identities

f(x) = cos x f(x) = sin x

EVEN ODD

sin sinx x csc cscx x

cos cosx x sec secx x

Problems

1) If sin (t) = ¼, find sin (-t).

2) If sin (t) is 3/8, find csc (-t).

3) If cos (t) = -3/4, find cos(-t).

cos cosx x

-1/4

If sin (t) is 3/8, then csc (t) = 8/3.

We want to find csc (-t) which is the opposite of csc (t) = -8/3.

cos(t) = cos(-t) so = -3/4

sec secx x sin sinx x

csc cscx x

Trig Identities

f(x) = tan x

ODD

tan tanx x

cot cotx x

If tan (t) = 2/3 find tan (-t).

-2/3

HW: WS 6-4