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**4.1 Radian and Degree measure**

Changing Degrees to Radians Linear speed Angular speed

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Definition of an angle An angle is made from two rays with a common initial point. In standard position the initial side is on the x axis

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**Positive angle vs. Negative angle**

Positive angles are Counter clockwise C.C.W. Negative angles are Clockwise C.W.

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**Angles with the same initial side and terminal side are coterminal.**

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**The measure of an angle is from initial side to terminal side**

Vertex at the origin (Center)

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Definition of a Radian Radian is the measure of the arc of a unit circle. Unit circle is a circle with a radius of 1.

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**The quadrants in terms of Radians**

What is the circumference of a circle with radius 1?

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**The quadrants in terms of Radians**

What is the circumference of a circle with radius 1?

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**The quadrants in terms of Radians**

The circumference can be cut into parts.

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**The quadrants in terms of Radians**

The circumference can be cut into parts.

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**Find the Coterminal Angle**

Since equals 0. it can be added or subtracted from any angle to find a coterminal angle. Given

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**Complementary Angles – two angles are complementary**

if their sum is 90 degrees or Supplementary Angles have a sum of 180 degrees or Find the complementary and supplementary angles for

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**Radian vs. Degree measurements**

360º = 180º = So or

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**Radian vs. Degree measurements**

360º = 180º = So or To convert Degrees into Radians multiply by To convert Radians into Degrees multiply by

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**Conversions: Radians Degrees**

To convert degrees to radians, multiply by To convert radians to degrees, multiply by Converting an angle from to decimal form.

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**Change 140º to Radians Change to degrees**

Use degree to rads. Use rads to degrees

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**How to use radian to find Arc length**

The geometry way was to find the circumference of the circle and multiply by the fraction. Central angle 360º In degrees Are length called S would be

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**How to use radian to find Arc length**

In degrees Are length called S would be In radian the equation is

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r = 9, θ = 215º Changing to rads Are length S

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**Linear speed and Angular speed**

Linear speed is Angular speed is Assuming “constant speed”

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**Consider a particle moving at a constant speed along a circular arc of **

Linear and Angular Speeds Consider a particle moving at a constant speed along a circular arc of radius r. If s is the length of the arc traveled in time t, then the linear speed v of the particle is Linear speed v Moreover, if is the angle (in radian measure) corresponding to the arc length s, then the angular speed (the lowercase Greek letter omega) of the particle is Angular speed A relationship between linear speed and angular speed is

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**where is measured in radians**

Area of a Sector of a Circle where is measured in radians A sprinkler on a golf course fairway is set to spray water over a distance of 70 feet and rotates through an angle of 120 degrees. Find the area of the fairway watered by the sprinkler. 120o = how many radians? 70 ft 79-99 odd, 107

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**Tip of the second hand as it passes around the clock face.**

Finding Linear Speed The second hand of a clock is 10.2 cm long. Find the linear speed of the Tip of the second hand as it passes around the clock face. Linear speed v Arc length s =1.068 cm/sec

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Angles and Radian Measure Section 4.1. Objectives Estimate the radian measure of an angle shown in a picture. Find a point on the unit circle given one.

Angles and Radian Measure Section 4.1. Objectives Estimate the radian measure of an angle shown in a picture. Find a point on the unit circle given one.

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