Lesson 5-1: Angles and Degree Measure

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Presentation transcript:

Lesson 5-1: Angles and Degree Measure LEQ - What are co-terminal angles and reference angles? Lesson 5-1: Angles and Degree Measure

Angles – two rays joined at a vertex 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: Positive angles are measured counter-clockwise Negative angle are measured clockwise Give the angle measurements for each of the following: 3 clockwise rotations 2.4 counterclockwise rotations

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.) 150º b.) -315º c.) 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.

latitude and longitude lines on earth Angle conversion Angles 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 conversion Angles are measures in degrees, minutes and second Angle conversion Angles 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 conversion Angles are measures in degrees, minutes and second Angle conversion Angles 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.

Graphing calculator: Convert 52.125º to degrees, minutes and seconds.

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