SECTION 2.3SECTION 2.3

EQ: Which of the trigonometric functions are positive and which are negative in each of the four quadrants?

Warm-Up/ActivatorWarm-Up/ActivatorName the quadrants of the

Coordinate (Cartesian) Plane – use drawing on next slide.

Label the signs of x and y in each quadrant

Which coordinate is sin and which coordinate is cos ?

Label the signs of the sine and cosine in each quadrant.

Drawing for the Drawing for the Warm-up/ActivatorWarm-up/Activator

A

Otan

cos

sin1

1

HAHO

H

H

cos

sintan

A

Otan

So, by multiplying the top and bottom of the fraction by 1/H it follows that

How does tangent relate to sine and cosine?

tan

cos

sin

+ +

+ -- -

- +

tan

cos

sin

tan

cos

sin

tan

cos

sin

A

CT

SP(cosΘ, sinΘ) ( x , y )

ALL STUDENTS TAKE CALCULUS

Reference Right TriangleReference Right TriangleDrop a perpendicular from the terminal side to the x-axis Drop a perpendicular from the terminal side to the x-axis and then you have a right triangle with the reference and then you have a right triangle with the reference angle as one of the acute angles.angle as one of the acute angles.

Starter Examples:Starter Examples:Find the reference angle for each of

the following, then determine the value of the function based on special or quadranal angles, and the location of the terminal side.

1) sin 300 ref < 60Sign - - sin 60

2) cos 150 30 - - cos 30

3) tan 225 45 + tan 45

12

3

2

3

Example 4Example 4Find the reference angle for each

angle given.(a)  210˚

(b)  135˚

(c)  422˚

Your Turn 4Your Turn 4Find the reference angle for each

angle given.(a)  160˚

(b)  285˚

(c)  600˚

Example 5 & Your Turn 5Example 5 & Your Turn 5Find the exact value of cos 210˚

Find the exact value of sin 330˚

Example 6 & Your Turn 6Example 6 & Your Turn 6Find the exact value of tan 495˚

Find the exact value of tan 660˚

Example 7 & Your Turn 7Example 7 & Your Turn 7Find the exact value of csc (-

210˚)

Find the exact value of sec (-330˚)

Example 8 & Your Turn 8Example 8 & Your Turn 8Find all values of where when

Find all values of where when

3600

2

3sin

3600 2

3cos

Example 9 & Your Turn 9Example 9 & Your Turn 9Use a calculator to approximate the

followinga) tan 466˚ b) csc (-313˚)

Use a calculator to approximate the following

a) sec (-118˚) b) cot (226˚)

Example 10 & Your Turn Example 10 & Your Turn 1010