CIE Centre A-level Pure Maths

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Presentation transcript:

CIE Centre A-level Pure Maths P1 Chapter 18 CIE Centre A-level Pure Maths © Adam Gibson

RADIANS The radian is useful to distinguish between quantities of different nature but the same dimension. For example angular velocity can be measured in radians per second (rad/s). The angle subtended at the center of a circle by an arc of circumference equal in length to the radius of the circle is one radian. Angle measures in radians are often given without any explicit unit. When a unit is given, sometimes the abbreviation rad is used There are 2π (approximately 6.28318531) radians in a complete circle.

RADIANS How can we convert between radians and degrees? or Using this conversion, find: 1 degree in radians = 0.01745… 1 radian in degrees = 57.2958..

Finding areas and arc lengths The ratio of the arc length to the circumference is the same as the ratio of the angle to 360 deg. A s θ r Can we use the same idea to find the area A … ? Remember these formulae – but only with radians!

Why measure angles in radians? Here is one reason (there are others … ). Suppose we want to calculate the first derivative of y = sinx at x = 0. We don’t have a simple formula, so let’s use the definition of derivative (limits): Put x = 0. What happens?

Why measure angles in radians? “arc” “chord” P r O θ A Q

Why measure angles in radians? Later, we will discuss the formula: which works only in radians. Now you should read carefully Example 18.2.1 on p. 266 and then do: Exercise 18A Q1 a,e,i Q2 a,e,i Q5, Q8, Q10