5-1 Angles and Degree Measures

Angles Angles can be formed by rotating a ray around a fixed endpoint, called the vertex.

If the rotation of the angle is counter-clockwise, then angle is positive If the rotation of the angle in clockwise, the angle in negative.

Standard Position When an angle is located on a coordinate plane, with the vertex at (0,0) and the initial side along the x-axis, the angle is in standard position

Remember...one full rotation is 360◦

Today, the most common way to measure an angle is in degrees Today, the most common way to measure an angle is in degrees. However, instead of using decimals, we can use minutes or seconds. This is often used for longitude and latitude 1 minute = 1/60 degree 1 second = 1/3600 of degree ( or 1 second = 1/60 of minute)

Practice. 1)Change 15.735° into minutes and seconds 2) 24.876 2) Change 39° 5’ 34’’ to a decimal rounded to the nearest thousandths.

Use google to find the latitudes and longitude of Jacksonville NC Use google to find the latitudes and longitude of Jacksonville NC. Then convert it to degrees and minutes. Send your answer to m.socrative.com

Practice Give the angle (in degress) that would represent 3) 5.5 rotations clockwise 4) 3.3 rotations counter-clockwise

Coterminal Angles Coterminal Angles: Have the same terminal side. Remember, if you keep rotating a full spin (360) you’ll end up in the same spot. Therefore, every angle has infinitely many coterminals angles. For any angle, α, then all angles with the measure α + 360k° will be coterminal

Practice: Identify all angles that are coterminal with each angle. Then give one positive, and one negative angle 5) 50° 6) 225°

Identify an angle between 0-360 that is coterminal with the following angles 7) 775° 8) -1297° 9) -890°

Reference Angle Reference Angles are acute angles formed between the terminal side on an angle and the x-axis. Hint: To find reference angle: Quad 1: α is same Quad 2: 180 – α Quad 3: α – 180 Quad 4: 360 - α

Practice: Find the reference angle for each angle: 10) 120° 11) -135° 12) 280°

Send your answer to socrative. Find the reference angle for 670 degrees?

13)On January 28, 1998, a satellite spotted a neutron star that spins at a rate of 62 times per second. Through how many degrees does this star rotate in a second? In a minute? In a day? 14) During the winder, a bike rider trains on a stationary bike. She warms up slowly, then increases to 95 rmp (rotations per minute) for 30 seconds. Through how many degrees will a point on the outside of the tire rotate during those 30 seconds?

Assignment: P.280 (1-17) Check for Understanding