7.3 Trigonometric Functions of Angles

Angle in Standard Position

Distance r from (x, y) to origin always (+)

r

(x, y)

x

y

y

x

2 2r x y

Six Trig Functions

sine

cosine

cosecantsiny

r

secant

tangent cotangent

cosx

r

tany

x

cscr

y

secr

x

cotx

y

Memorize!!

Ex 1) Determine exact values of 6 trig functs of an angle in stand. pos. if term. side goes through (12, –5)

12 5x y

2 2(12) ( 5)r 169 13r –512

(12, –5)

siny

r

cosx

r

tany

x

cscr

y

secr

x

cotx

y

5

13

12

13

5

12

13

5

13

12

12

5

Signs of Trig Functions

I( +, + )

r is always (+)

sin & csc → sign of y

cos & sec → sign of x

tan & cot → both x & y- same sign → (+)- opp sign → (–)

II( – , + )

III( – , – )

IV( + , – )

x

y

AS

T C

Ex 2) If cos < 0 and tan < 0, in which quadrant does terminate?

cos < 0 → x < 0

tan < 0 → x & y have opp. signs

x < 0 → y > 0

→ Quadrant II

Homework

#704 Pg. 406 1 – 7 odd, 17 – 25 odd, 20, 26 &

Memorize 6 Trig Functions