Trigonometry

Trigonometry

Functions

Special angle of 30

Sin: 1/2
Cos: √3/2
Tan: 1/√3

Special angle of 0

Sin: 0
Cos: 1
Tan: 0

Special angle of 45

Sin: 1/√2
Cos: 1/√2
Tan: 1

Special angle of 60

Sin: √3/2
Cos: 1/2
Tan: 1

Special angle of 90

Sin: 1
Cos: 0
Tan: math error

Trigonometric ratios

Sin: Opp/Hyp
Cos: Adj/Hyp
Tan: Opp/Adj

Reciprocal ratios

cscθ = 1/sinθ
secθ = 1/cosθ
cotθ = 1/tanθ

What is the related acute angle (R.A.A)?

Between the terminal arm and the x-axis, if there is no known RAA stated it's in quadrant 1

What is the principal angle?

The angle that is formed between the positive x-axis and the terminal arm in standard position. Angles that are positive are measured in a clockwise direction

Quotient identity

Tanθ = sinθ/cosθ
Tan2θ= sin2θ/cos2θ

Pythagorean identity

Sin2θ + cos2θ = 1
Alternate form:
Sin2θ = 1=cos2θ or Cos2θ = 1-sin2θ

Reciprocal identities

cscθ = 1/sinθ
secθ = 1/cosθ
cotθ = 1/tanθ

Sine law

The sine law states that the ratios of each side of any triangle ABC to the sine of its opposite angle are equal. There must be one complete set of numbers known in order to use the sine law (angle A and side a)

When sine can be used

1. When two angles and any side of the triangle are known; angle, angle, side or angle, side, angle (AAS, ASA)

2. Two sides and an opposite angle; side, side, angle (SSA). This is called the ambiguous case, because multiple triangle can be created/drawn, if the opposite side to θ is greater than the height of the triangle but less than the other side there will be two triangle (2 triangles occurs when b(sinA)

When can cosine law be used?

Used when there is a non-right angle triangle and/or a complete ratio is not present. There must be two sides with a contained angle or when there are three sides and no angles

Word problems

Steps:
1. Draw a diagram
2. If it's a right angle triangle use pythagoras (SOHCAHTOA)
or if there is a side/angle pair use sine law, if not use cosine law
3. Therefore statement