Adamson University Chemical Engineering Society

RalphEdreanOmadto|2012

TRIGONOMETRY

- The branch of mathematics that deals with

the relationships between the sides and the

angles of triangles and the calculations

based on them, particularly the

trigonometric functions.

CONVERSIONS

a.) Degree to Radians

b.) Radians to Degree

Rotational speed (N) - No. of Revolution per minute

Angular speed (ω) - 2

]

Linear speed (V) - 2 or ω

Coupled Wheels

ω

ω

Concentric Wheels

ω

ω

SIX TRIGONOMETRIC RATIOS:

sin A =

csc A =

cos A =

sec A =

tan A =

cot A =

SOHCAHTOA

SOH- Sine Opposite over Hypotenuse

CAH- Cosine Adjacent over Hypotenuse

TOA- Tangent Opposite over Adjacent

Angle of Elevation

- The angle of elevation of an object as seen

by an observer is the angle between the

horizontal and the line from the object to the

observer's eye (the line of sight)

Angle of Depression

- If the object is below the level of the

observer, then the angle between the

horizontal and the observer's line of sight

Co-terminal Angles

- Coterminal angles are angles in standard

position (angles with the initial side on the

positive x-axis) that have a common

terminal side. For example 30°, –330° and

390° are all coterminal.

Quadrantal Angles

- An angle in standard position with terminal

side lying on x-axis or y-axis is called as

Quadrantal Angle.

TRIGONOMETRIC IDENTITIES

Reciprocal Identities

sin θ = 1

csc θ csc θ =

1

sin θ

cos θ = 1

sec θ sec θ =

1

cos θ

tan θ = 1

cot θ cot θ =

1

tan θ

Pythagorean Identities

a) sin²θ + cos²θ = 1

b) 1 + tan²θ = sec²θ

c) 1 + cot²θ = csc ²θ

Adamson University Chemical Engineering Society

RalphEdreanOmadto|2012

Quotient Identities

Angle-Sum and -Difference Identities

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

sin(α – β) = sin(α)cos(β) – cos(α)sin(β)

cos(α + β) = cos(α)cos(β) – sin(α)sin(β)

cos(α – β) = cos(α)cos(β) + sin(α)sin(β)

Double-Angle Identities

sin(2x) = 2sin(x)cos(x)

cos(2x) = cos2(x) – sin

2(x) = 1 – 2sin

2(x) = 2cos

2(x) -1

Half-Angle Identities

The above

identities can be re-stated as:

sin2(x) = ½[1 – cos(2x)]

cos2(x) = ½[1 + cos(2x)]

Sum to Product Identities

Product to Sum Identities

AREA OF TRIANGLE

Heron’s Formula:

AREA OF A SEGMENT

AREA OF SECTOR

LAW OF SINES

If a < bsinA, no triangle.

If a = bsinA, 1 triangle (right)

If a > bsinA, 2 triangles

LAW OF COSINES

c2 = a

2 + b

2 – 2ab cos C

a2 = b

2 + c

2 – 2bc cos A

b2 = a

2 + c

2 – 2ac cos B

Adamson University Chemical Engineering Society

RalphEdreanOmadto|2012

LOGARITHM

- Inverse of Exponential Form

-

Properties of Logarithm

1.

2.

3.

4.

5.

6.

7.

Change of Base Formula

Natural Number (

- The number e is an important mathematical

constant, approximately equal to 2.71828,

that is the base of the natural logarithm

Properties of Natural Number

1.

2.

3.

4.

5. 6.

7.

SPHERICAL TRIGONOMETRY

- Spherical trigonometry is a branch

of spherical geometry which deals

with polygons (especially triangles) on

the sphere and the relationships between

the sides and the angles. This is of great

importance for calculations

in astronomy and earth-surface, orbital and

space navigation.