13.2 notes day 2
May 22, 2014
General Angles and Radian Measure
What if the triangle is not a 90 o triangle?
General Angles and Radian Measure
You can generate any angle by fixing one ray and rotating the other ray about the vertex. 900
terminal side
What is the definition of an angle?
1800
00
initial side
3600
2700
STANDARD POSITION
Coterminal Angles
General Angles and Radian Measure
Draw an angle with the given measures in standard position.
a. 2100
1500 and 5100 are called coterminal angles. Angles are coterminal if their terminal sides coincide. You can find coterminal angles by adding or subtracting multiples of 3600.
b. ­450 c. 5100
Find one positive and one negative coterminal angle to the given angles. a. ­600
b. 4950
13.2 notes day 2
May 22, 2014
Radians
Radians
Given a circle with radius r, a radian is the measure of an angle in standard position whose terminal side intercepts an arc length of r. We can rewrite degrees into radians and vice versa.
3600 = 2 radians
y
To rewrite a degree into radians, multiply by radians
r
r
1800
x
To rewrite radians into degrees, multiply by 1800
radians How many radians are there in a whole circle?
Radians
Convert 1100 into radians
Convert ­ into degrees Unit Circle
SPECIAL ANGLES FROM 0 to 360
13.2 notes day 2
Evaluating Functions
How to use the calculator
Fining an angle on the Unit Circle
If i spun in a circle and made 2/5 rotations, what angle did i spin in degrees and radians?
May 22, 2014
Fining an angle in radians on the Unit Circle
Where would 9 /4 be on the unit circle?
Arc Length
A sector is a region of a circle bounded by 2 radii and an arc of the circle.
r
arc length
central angle
r
The central angle of a sector is the angle formed by the 2 radii. 13.2 notes day 2
Arc Length and area of a Sector
Arc Length: s = r0
Area: A = 1/2 r20
Arc Length and area of a Sector
The restaurant at the Space Needle is circular and has a radius of 47.25 feet. The dining part revolves making a complete revolution in 1 hour. You go to dinner at the space needle and sit on the outside of the restaurant at 6:42 pm. If your dinner ends at 8:18 pm, through what angle did you rotate? How many feet did you revolve? May 22, 2014
Arc Length and area of a Sector
Find the arc length and area of a sector with a radius of 9 cm and a central angle of 600