Entry #: rt

Example: Complete the following table using the triangle below.

t'*#'tr'Q+'r.'.]fr-"frn' 'TL

$ t:|4*x

Special Right Triangles

Lesson 6,2 & 6.3: Right Triangle Trig & Trigonometric Functions of Angles

Trieonometric Ratios of Rieht Triansles

$\n($=ryryf ctc(g\=;ffi;- r adsaceh\

cor(S)= ]F.ran(s)=ffik cor(s)=m

3sin(0) = b csc(0) =

J

3

cos(a) = t sec(0) =E\

tan(g) = -q cot(g) = q

1. lsosceles Right Triangle450-450-900

2. 300 - 500 - 90"

x{T

od5acen\

Trisonometric Functions of Aneles

Let POQ be a right triangle with an acute angle 0.

e(1(

$

)T) xz + $t= f"*Y={Try$\n(g) =teot (s) = +ran(s) =*

(^r * o)

c$c($= +rec(s)= +cot(o)= f

(r5 * o)

Rgfgrencq Angles

Let 6 be an angle in standard position. fhe YQ,Q eV e(\ Ce angle d associatedwith 0 is the acute angle formed by the terminal side of 0 and the x-axis.

Example: Find the reference angle for the following angles.

x

Zrr-Hh $ '1.51.k - a

5t5

\t0'0/ ?-s

2-.&r\ 2-'nJ

Evaluating Trigonometric Functions for Any Angle

1. Find l.he reQerer\ce a\Nq\e\)

2. E\a\qa\e lhe \ri$ SrmCnon

l. g=Y3

2. 870" 6 = \te".. -*"S*t.li t1$

- \60"6=5nf qo" = 3d

Q"/ 3ts"

E.

a\ E.

'^$\$,ffi-l

2-lo"

Example: Use the reference angle to evaluate the following trigonometric functions.

s -- 1q0" *\%s"

1-ro'

3. sin(T)

= G0"

0/tGo"

t\r., (bo") - YB\n(L\s"\ = -E

-..^ /\s4\- -trb\rr1 3,- L

b/as6n'- H-a%

C;+ trnQ\=;

g = \$b"- "-o= (aU

*\r0"

E=\t$-ttsj.-sa ql)o/atoo"

cot (\5") = \qo \"(\qb") * *t

sec (- t\ = ST

$ec (t) =

b /zst_5-t\

1-g{z \zE.L

r\eArea of a Triangle Using Trigonometry

Example: Find the area of the triangle ABC shown below.

^4 \ = t (ro\ (t\ %\n (\10')

\=\(tt)(YlA r t:(EA* 1- Cmt

o/ts

E-,:: L

A= i ,btrn(g)urhexe a b b

\n a \rian3\etve t\de \eng\\3

6d\acen\ *o S

trn tt"$]

$