Radians ch 5 Flashcards
What is the formula for arc length?
Theta x radius (when theta is in radians mode)
What is the difference between a major arc and a minor arc?
A major arc has the majority of the angle round the point at the centre of the circle whereas the minor arc has a smaller angle.
What is the difference between a sector and a segment?
Sector is the area enclosed by two radii.
Segment is the area enclosed by a chord and perimeter.
What is the formula for area of a sector?
1/2r^2 x theeta.
How do you work out the area of a segment?
Area of sector - area of triangle.
Why does the small angle approximations work for sin?
Because for very small values of theta the sin curve is very similar to the y=theeta curve.
What is the small angle approximation for sin?
When theta is small and measured in radians, sintheta is approx theta
Why do the small angle approximations work for cos?
Because for small values of theta, cos curve tends to 1-1/2theta^2
What is the small angle approximation for cos?
Costheeta is approx 1-1/2theeta^2
why does the small angle approximations work for tan?
Because for very small values of theta, y=theeta tends towards tantheeta
How would you deal with a cos4theeta in small angle approximation?
Sub in 4 theta for theta in cos.
How would you state the approximate value of 2theta^2+7theta-1?
Take all the theta as 0 or negligible so answer would be -1
