Trigonometry Day 1 ( Covers Topics in 4.1) 5 Notecards

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Trigonometry Day 1 ( Covers Topics in 4.1) 5 Notecards Chapter 4 Trigonometry Day 1 ( Covers Topics in 4.1) 5 Notecards

Angles Positive Angle (counterclockwise) Terminal side Initial side Terminal side Positive Angle (counterclockwise) Negative Angle (clockwise) 90˚ For example, on the coordinate plane: 130˚ 180˚ 0˚ is the positive x-axis 360˚ -70˚ Angles 270˚

What is a Radian? A radian is the measure of the central angle  that intercepts an arc c equal in length to the radius of the circle: 2 radians 1 radian The radius of the circle fits around the circumference 6.28 times ( 2π ). 3 radians 4 radians 6 radians Radian 5 radians

Quadrants:

Coterminal Angles Two angles are coterminal if they have the same initial side and terminal side ** To find coterminal angles, either add or subtract 2π or 360°. Coterminal Angles

Ex1: Find a positive and a negative coterminal angle for 125°. Ex 2: Find a positive and negative coterminal angle for 125+360=485° 125-360=-235 °

Converting between Radians and Degrees from Degrees to Radians Multiply by from Radians to Degrees Converting between Radians and Degrees

3π/2 3π/4 120˚ 225˚ Ex1: Change 270° into radians Ex 3: Change into degrees Ex 4: Change into degrees 3π/2 3π/4 120˚ 225˚

Arc Length For a circle of radius r, a central angle  ( in radians) intercepts an arc of length s: S = r  ( is in radians) S  r Arc Length

Ex 1: What is the arc length of a sector if r=4 inches and =240º (Remember- you must convert to radians first)

You will now do a plate activity with your teacher . Sketching Angles You will now do a plate activity with your teacher .

Sketching an angle Sketch a graph of the following angles: 273º 2. 3.1000 º