Chapter 4

Trigonometry Day 2

(Covers a variety of topics in 4.2-4.4)

6 Notecards

Six Trig Functions

sin opposite

hypotenuse

cos adjacent

hypotenuse

tan opposite

adjacent

csc hypotenuse

opposite

These are the reciprocal functions

sec hypotenuse

adjacent

cot adjacent

opposite

Six Trig Functions (continued on next slide)

To remember your trig functions:

SOHCAHTOAAnother Trig Property you need to know:

tan sincos

Ex 1: sin = 3/5

Find the other trig functions:

cos = _______

tan = _______

csc = ________

sec = ________

cot = ________

Ex 2:

Find the other trig functions:

sin = _______

cos = _______

csc = ________

sec = ________

cot = ________

tan 3

3

Suppose I give you a point on the Unit Circle:

12

13, 5

13

Any point on a unit circle (when radius is 1) is in the form

(cos,sin)Therefore:

sin 5

13& cos

12

13

tan = ______ csc = ______ sec = ______ cot = _____

•

Basic Trig Functions

1

3

260°

30°

12

1

Degrees Radians Sin Cos tan

30

45

60

64

3

1

2

1

2

3

2

3

2

3

3

3

2

2

2

21

(1,0)

(0,1)

(-1,0)

(0,-1)

90°

180°

270°

0°/360°

Use the unit circle, with a radius of 1, to figure out your trig functions for the Quadrant angles 0,90,180,270,360

Remember:

tan sincos

And that all points on a unit circle are in the form of

cos,sin

AS

T C

When doing Trig Functions in each quadrant, some functions ( and their reciprocals) are positive and some might be negative:

Here is the phrase to remember this in the quadrants:

All Students Take Calculus

Signs (+/-) of Trig functions in QuadrantsContinued on next slide

• “A” means that in the first quadrant all the trig functions are positive: SIN, COS, TAN

• “S” means that in the second quadrant only the SIN is positive, and the COS and TAN are negative

• “T” means that in the third quadrant only the TAN is positive, and the SIN and COS are negative

• “C” means that in the fourth quadrant only the COS is positive, and the TAN and SIN are negative

Continued from previous slide

Reference Angles

You will use reference angles to help you figure out the value of trig functions

Your reference angle is the angle between the terminal side and either the 180° line or the 0°/360° line

Reference Angles

Find the reference angle for the following:

1)602)2503)300

4)56

5)23

6)5554

Even and Odd Trig Functions

Cosine and Secant are EVEN:

cos(-t) = cos (t) sec(-t) = sec (t)

Sine, Cosine, Tangent, and Cotangent are ODD:

sin(-t) = - sin(t) csc(-t) = - csc(t)

tan(-t) = - tan(t) cot(-t) = - cot(t)

For example: sin(t) = 1/5, so sin(-t) = -1/5

If cos(t) = 2/3 , then cos(π+t) = -2/3