Lesson 5-1:Angles and Degree Measure

LEQ - What are co-terminal angles and reference angles?

Angles – two rays joined at a vertex. Angle are measured in degrees, minutes and seconds.

Standard Position – all angles in the coordinate plane have their initial side on the x-axis.

Give the angle measurements for each of the following:

3 clockwise rotations

2.4 counterclockwise rotations

Positive angles are measured counter-clockwiseNegative angle are measured clockwise

Reference Angle – positive, acute angle formed between terminal side and x-axis.

In your notes, sketch each angle and indicate the reference angle measure:a.) 150ºb.) -315ºc.) 225º

Quadrantal Angles – angles whose terminal side lies on the axes.

Coterminal angles – angles which differ by 360º and have the same terminal side.

If αis the degree measure of an angle, then all angles meas°, where k is an integer, are coterminal with α.

Ex. Identify all angles coterminal with 45°

Coterminal angles – angles which differ by 360º and have the same terminal side.

If 775º is in standard position, Determine a coterminal angle that is between 0 and 360º. State the quadrant in which the terminal side lies.

If -777º is in standard position, Determine a coterminal angle that is between 0 and 360º. State the quadrant in which the terminal side lies.

Angle conversionAngles are measures in degrees, minutes and second. A minute is 1/60 of a degree and a second is 1/60 of a minute. (ex. 32º 5' 2.34" )

latitude and

longitude lines on earth

Angle conversionAngles are measures in degrees, minutes and second. A minute is 1/60 of a degree and a second is 1/60 of a minute. (ex. 32º 5' 2.34" )• Example: Convert 329.125° to degrees,

minutes and seconds.• 329° + (0.125 60)• 329° + 7’ + (0.5 60)• 329° + 7’ + 30”

• Example: Convert 15.735° to degrees, minutes and seconds.

Angle conversionAngles are measures in degrees, minutes and second. A minute is 1/60 of a degree and a second is 1/60 of a minute. (ex. 32º 5' 2.34" )

• Example: Convert 39°.5’34” to a decimal, (just degrees).

What is the high school’s latitude and longitude?

Convert latitude and longitude to just degrees.

Angle Conversion: Convert 52.125º to degrees, minutes and

seconds.

Convert 87.234º to degrees, minutes and seconds.

Convert 13º 5' 3“ to degrees.

Graphing calculator:

Convert 52.125º to degrees, minutes and seconds.

Convert 87.234º to degrees, minutes and seconds.

Convert 13º 5' 3“ to degrees.

LESSON VOCABULARY REVIEW

Vertex Initial side Terminal side Degrees Minutes Seconds Quadrantial Angle Co-terminal Angle