PARTS OF ANGLES AND DMS

Fall, 2015

Dr. Shildneck

Angles and Their Measures

Recall that an angle is defined as two non colinear rays that ‐share a common endpoint, called the v ertex.

An angle in (circle) trigonometry has a fixed (starting) side, called the i nitial side ‐ which points in the direction of the positive x‐axis.

The v ertex is the origin.

The second side is rotated (like the hands of a clock) about the vertex. This side is called the t erminal side.

An angle with this placement is said to be in S tandard Position. 2

y

terminal side

initial side

x

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The measure of the angle describes the amount and

direction of the rotation necessary to move from the initial side to the terminal side.

A positive angle indicates that the terminal side has been rotated counter clockwise.‐

A negative angle indicates that the terminal side has been rotated clockwise.

y

x

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Positive Angle

Negative Angle

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The most common angular unit of measure is called the "degree," which is equivalent to 1/360 of a full rotation around a circle.

Key (basic) Angle Measures (counterclockwise)

• 0o ‐ No rotation• 90o ¼ ‐ of a rotation • 180o ‐ ½ of a rotation• 270o ¾ ‐ of a rotation• 360o ‐ 1 full rotation (back to the

initial side)

These angles are called the "Quadrantal Angles" since they end on the boundaries between the quadrants of the coordinate plane.

Angles based on rotation can be any size and either sign (positive or negative).

If you were to continue to rotate the terminal side past 360o, you would simply continue to add (or subtract if negative) to the angle.

**Note that Additional rotations are indicated by a rotation mark.

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120o

-240o

Degrees – Not exact

Obviously the terminal side can end up not on a "degree" mark. Thus, you can have measures that use parts of a degree.There are two ways that this might be indicated.

1. Decimal form: This form simply indicates the "fractional" part of the degree.

Example: 35.75o ‐ means 35 degrees and 3/4 more of a degree

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2. Degrees-Minutes-Seconds (DMS)A more formal "part form" of a degree uses minutes and seconds.

The conversion ratio between decimal form and DMS is like that of a clock.

1 degree is made up of 60 minutes ( 1o = 60') 1

minute is made up of 60 seconds (1' = 60")

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Converting by Hand

Convert 65.755o into DMS form

Convert 20o 21' into Decimal form

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Converting by Calculator

Convert 65.75382o into DMS form

Convert 20o15' 54" into Decimal form

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ASSIGNMENT 2

WS ‐ Measures of Angles