What is a radian?
The amount of rotation required such that the length of the intercepted arc is equal to the radius.
Angles
- Angle- Two rays with a common endpoint. Angles are determined by rotating a ray about it's endpoint.
- Initial Side- The starting position of the ray when measuring an angle
- Terminal Side- The position after the roation of a ray
- An angle can be positive or negative
- How do we tell if it's positive or negative? Angles are in standard position, where the vertex is at the origin, and the initial side is at the x-axis
- Negative angles by clockwise rotation.
- Can be measured in degrees or radians
Angle Relationships
- Congruent- Angles with equal measures
- Complementary- Angles with measures that add up to 90
(or π/2 radians)° - Supplementary- Angles with measures that add up to 180
(or π radians)° - Coterminal- Two angles that when put in stardard position have terminal sides at the same spot
Coterminal angles
Arc Length
A circle has a radius of 4 inches. Find the length of the arc intercepted by a central angle of 240°.
First, convert 240° to radians
240° = 240° ( π radians/180°)
4 π/ 3 radians
s=rθ
= 4(4π/3)
=16π/3
= about 16.76 inches
Converting degrees to radians
to convert degrees to radians, multiply degrees by π radians/180°( to cancel out the degrees)
135° =135 * (π radians/180°)= 3π/4 radians
Converting radians to degrees
to convert radians to degrees, multiply degrees by 180°/π radians (to cancal out the radians)
2 radians = 2 radians * (180°/ π radians ) = 114.59°
No comments:
Post a Comment