MAT 1275: College Algebra and Trigonometry (Lectures 15), Assignments of Mathematics

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Session 15 Trigonometric function

forrighttrianglesy

Consider the

right triangle bP opposite 4

Adjacent

Given the above

diagram we (^) define

the

trigonometric

functions of

sine (^) cosine

and

tangent

Sino Opposite

Hypotenuse

c

tan

a Opposite Adjacent

These

formulas can

be

memorized

with the acronym

SOH CAH TO A

Ex

ample Find^ sine cosine (^) and tangent o angles A (^) and B 5 4 13 sin (^) A

sinB (^) opP I hyp

hyp

5 Cos (^) A adj (^4)

costs

adj hyp

Typ t

an A

17

tan B

OPI adj

adj'T

B

Examp sD^ Find^ sine cosine and^ tangent of angles

A and B

FK GE 12

Sin A

opp

Typi

I sinB

I

13 B

cos A adj 5 cos Bil

hyp 13

tan A^

I

tan D I

adj (^5 ) D

we may

re wrinte tan 300_

f by rationalizing

the

denominator

tan3oo

BE Bz

Now we

consider

the 45

triangle til

sin 450

tr rt (^) II

Cos 450 I^ Fz

ra z

tan 45 u^

I

Tha t^

is

sin (^450) fz FE Ccs (^450)

tan 45 o^ I

we (^) know sin (^170 13) 15C D 13T^ sin 170 513

BT

tg.IN

onh4.

w e k^ n^ o^ w

an 170

ftp.ta

toT 42

y

ME

Examplem class C

LIB A

F in

d L (^) B (^) AT and (^) AIT g

ta t^ C^ B t^ L^ C^1800

900 LB^ t^730

D L^ B^

t 1630

D 1LB

we have

Sin 730

ATI

16

D AT

1Gsin

T15.

D BT

FT 16.

We

now find^ LB using rig an (^) B

A

y

D B tan

Next

we find Lei

using the fact that At LB^

1 E^ c^1800

900 117.^

1 L^ C^180

s Le^ 72. Thus 132

C (^) 72.60 (^) DM Examplecci

B 16

c

A

Find

AT LB and LC^

4 we first^ find^ AT using

the

Pythagorean

Theorem

AB AT (^) BIZ

cos B

ABI (^) I L

At 16

4

D B^ cos t

4

We may now (^) find

using the (^) fact that Atl Btcc 1860 D 900 (^755) TLC 1200 D 165.^ a Lc 120 D LC (^) 14. B (^16)

Thus 4

C A 15. Dk

Trigonometric Applications Jr

angle

of

ion

t g1e of

depression

an 200 b

200

D h Zoo

tan 200 I

D The^

height

of the

tree (^) is

72.79 ft

Exam

ple class (^) A giraffe's shadow is

8 meters

How tall^ is

the giraffe if (^) the angle

of

elevation to the^ sun^ is 280 s n 28 r I 8M 1

an 280 I