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By: Mckenzie & Adriana

Trigononometry

[trig-uh-nom-i-tree]

Noun

Bibliography

http://serc.carleton.edu/mathyouneed/trigonometry/index.html

http://dictionary.reference.com/browse/trigonometry

https://en.wikipedia.org/wiki/Law_of_sines

The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

(according to dictionary.com)

Trigonometric Ratios

The CAST rule tells you which function is positive in each quadrant

Grade 10 Review

In this quadrant, everything will be positive

In this quadrant, only sine will be positive

(Sine)

(All)

S

A

2

3

1

4

C

T

(Cosine)

(Tangent)

In this quadrant, only cosine will be positive

In this quadrant, only tangent will be positive

SOH

Sine = Opposite/Hypotenuse

CAH

Cosine = Adjacent/Hypotenuse

TOA

Tangent = Opposite/Adjacent

Angles

The Terminal Arm forms the angle

The Cosine Law

Terminal Arm

The Cosine Law is used for solving triangles.

Reference Angle

  • the angle formed between the terminal armand the x-axis
  • less than 90°
  • has a positive value

Reference Angle

To find a side:

1

2

a²=((b²+c²)- (2bc cosA))

Right Angle Triangles

THE SINE LAW

SinA SinB SinC

____ = ____ = ____

a b c

a b c

____ = ____ = ____

SinA SinB SinC

An equation relating the lengths of the sides of any shaped triangle to the sines of its angles

Ambiguous Cases

Initial Arm

4

3

C

The Initial Arm is the arm that is on the x-axis

a

b

= Standard Angle

s

180°

B

A

= Reference Angle

c

R

150°

To find an angle:

cosA = (b²+c²-a²/2bc)

30°

180°-150°=30°

Special Triangles

"Count to Three"

B

*Use angles to find exact values

"Count To Three"

(60°)

30°-60°-90°

Isosceles

a

Sin30° = 1/2

Cos30° = 3/2

Tan30° = 1/ 3

Sin45° = 1/ 2

Cos45° = 1/ 2

Tan45° = 1

c

TOA

CAH

SOH

Finding Exact Values Using Angles

(90°)

(30°)

C

A

Sin60° = 3/2

Cos60° = 1/2

Tan60° = 3

b

'A' is usually used as the reference angle

Isosceles

B

(45°)

45° - 45° - 90°

a

c

2

TOA

CAH

SOH

1

2

1

Mind Map

(90°)

(45°)

C

A

b

1

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