Transcript 5-1 Angles and Degree Measures

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.
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. 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 3: α – 180
Quad 2: 180 – α
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