7. applications of trigonometry

7.7. Applications of Trigonometry Applications of Trigonometry

Sine Formula

Cosine Formula

sin sin sina b c

A B C

2 2 2cos

2b c aA

bc

2 2 2cos

2a c bB

ac

2 2 2cos

2a b cC

ab

a2 = b2 + c2 - 2bc cos A

b2 = a2 + c2 - 2ac cos B

c2 = a2 + b2 - 2ab cos C

A B

C

c

ab

(a) How to memorize the sine formula and the cosine formula?

A B

C

c

abSine Formula

Sine Formula Easy Memory Tips:

sin sin sina b c

A B C

A and a, B and b, C and c.

Where a, b and c represent the opposite sides of the angles A, B and


C respectively.

aA C

cbB

A

a

C

c

b

BOpposite sideOpposite side

Oppositeside

In the formula, the alphabets of the numerator and the denominatorare the same, like

A B

C

c

abCosine Formula Easy Memory Tips:

Cosine Formula

c2 = a2 + b2 - 2ab cos C2 2 2

cos2

a b cCab

1. Put C on the L.H.S.

2. Put the opposite side c of the

cos( ) =c

( )2+( )2-( )2

2( ) ( )

3. Put the remaining sides inthe remaining brackets

ab ab

Suppose the required angle is C.

C

Remember the position of each symbol

(a) How to memorize the sine formula and the cosine formula?


angle C in the bracket afterthe minus sign

(b) When to use the sine formula or the cosine formula?

A B

CCase I: two sides and the included angle are given

Easy Memory Tips:

included angle are given” as SAS.We can denote “two sides and the

SAS

The two S represent the given two sidesAC

A represents the given angle

and BC,

C.


　 Using to find the length of AB.c2 = a2 + b2 - 2ab cos C

(Except the two cases below, the sine formula is preferred)

B

A B

CCase II: three sides are givenCase II: three sides are given

Easy Memory Tips:

We can denote “three sides are given” as SSS.SSS

Using to find . cos =2 + 2 2

2A

abbc

cbcb

bC a

aBAC

(b) When to use the sine formula or the cosine formula?(Except the two cases below, the sine formula is preferred)


7. applications of trigonometry

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