Chapter 5 – Trigonometric Functions Section 1 – Angles and Degree Measure

Angle Basics If you draw an angle on the coordinate plane and the initial side falls on the x-axis, this is called standard position.

Angles Angles are traditionally measured in degrees. A full rotation of an angle around the origin results in a 360 degree angle. EX 1: Give the measure of an angle that is rotated 5.5 times clockwise. EX 2: Give the measure of an angle that is rotated 3.3 times counterclockwise.

Coterminal Angles Angles are coterminal if they would be drawn in the exact same position. For examples, 30 degrees and 390 degrees are coterminal, because they are separated by 360 degrees. EX 3: Find one positive and one negative angle that are coterminal with 225 degrees.

Converting Decimals to Minutes and Seconds Normally, we might write degrees with decimals, such as 135.62 degrees. However, it is more common to write angles with minutes and seconds To find minutes and seconds from decimal degrees: multiply degree decimal by 60 for the minutes and then if there is STILL a decimal, multiply THAT decimal part by 60 for the seconds

Converting Decimals to Minutes and Seconds EX 4: Convert 15.735 degrees to degrees, minutes, and seconds. To convert the other way, divide minutes by 60 and divide seconds by 3600 and add the results to the original degrees. EX 5: Convert 39 degrees,5 minutes, and 34 seconds to a decimal rounded to the nearest thousandth.

Assignment Chapter 5, Section 1 pgs 280-281 #5-12,18-40E