Pure Year 2 Unit 5 Flashcards
What is a radian?
A measure of angles
1 radian = the angle AOB of the radius of a segment with equal arc length and radius
What is 2pi radians in degrees
360
What is pi radians in degrees
180
What is 1 radians in degrees
180/pi
Convert 30’ to radians
pi/6
Convert 45’ to radians
pi/4
Convert 60’ to radians
pi/3
Convert 90’ to radians
pi/2
Convert 180’ to radians
pi
Convert 360’ to radians
2pi
sin(pi/6)
1/2
sin(pi/3)
root(3)/2
sin(pi/4)
root(2)/2
cos(pi/6)
root(3)/2
cos(pi/3)
1/2
cos(pi/4)
root(2)/2
tan(pi/6)
root(3)/3
tan(pi/3)
root(3)
tan(pi/4)
1
sin(pi-theta)
sin(theta)
sin(pi+ theta)
-sin(theta)
sim(2pi - theta)
-sin(theta)
cos(pi-theta)
-cos(theta)
cos(pi+theta)
-cos(theta)
cos(2pi-theta)
cos(theta)
tan(pi-theta)
-tan(theta)
tan(pi+theta)
tan(theta)
tan(2pi-theta)
-tan(theta)
Arc length formula in radians
l = r(theta)
Area of a sector in radians
A = (1/2)(r^2)(theta)
When theta is small and in radians, sin(theta) =
theta
When theta is small and in radians, tan(theta) =
theta
When theta is small and in radians, cos(theta) =
1-((theta^2)/2)
