U8D4 Have out: pencil, red pen, highlighter, notebook, calculator, assignment Bellwork: 1. Convert the following angles from degrees to radians. a) 30 b) 45 +2 +2 2. Convert the following from radians to degrees. a) b) +2 +2 total:

Radian Values for Common Angles Part 1: Record the degree measures for all multiples of 30° and 45°. 90˚ 120 ˚ 60˚ 135 ˚ 45˚ 150 ˚ 30˚ Use a pencil!!! 180 ˚ 0˚ 360 ˚ 210 ˚ 330 ˚ 225 ˚ 315 ˚ 300 ˚ 240 ˚ 270 ˚

Radian Values for Common Angles Part 2: Radians. Use multiples of these values to fill in the radian equivalent for each angle. 90˚ 120 ˚ 60˚ 135 ˚ 45˚ 30° = 150 ˚ 30˚ 45° = 180 ˚ 0˚ 360 ˚ on the bottom of the worksheet 210 ˚ 330 ˚ 225 ˚ 315 ˚ 300 ˚ 240 ˚ 270 ˚

now reduce the fractions 30° = 90˚ 120 ˚ 60˚ 135 ˚ 45˚ 150 ˚ 30˚ now reduce the fractions 180 ˚ 0˚ 360 ˚ 210 ˚ 330 ˚ 225 ˚ 315 ˚ 300 ˚ 240 ˚ 270 ˚

30° = 90˚ 120 ˚ 60˚ 135 ˚ 45˚ 150 ˚ 30˚ 180 ˚ 0˚ 360 ˚ 210 ˚ 330 ˚ 225 ˚ 315 ˚ 300 ˚ 240 ˚ 270 ˚

now reduce the fractions 45° = 90˚ 120 ˚ 60˚ 135 ˚ 45˚ 150 ˚ 30˚ now reduce the fractions 180 ˚ 0˚ 360 ˚ 210 ˚ 330 ˚ 225 ˚ 315 ˚ 300 ˚ 240 ˚ 270 ˚

45° = 90˚ 120 ˚ 60˚ 135 ˚ 45˚ 150 ˚ 30˚ 180 ˚ 0˚ 360 ˚ 210 ˚ 330 ˚ 225 ˚ 315 ˚ 300 ˚ 240 ˚ 270 ˚

This will be your first quiz on Tuesday!!! 90˚ 120 ˚ 60˚ 135 ˚ 45˚ 150 ˚ 30˚ Memorize this diagram. This will be your first quiz on Tuesday!!! 180 ˚ 0˚ 360 ˚ 210 ˚ 330 ˚ 225 ˚ 315 ˚ 300 ˚ 240 ˚ 270 ˚

Label the sides of the right triangle. Example # 1: The point (3, 4) is on the terminal side of angle θ in standard position. Plot (3, 4) and draw θ. y x Let r be the length of the segment from (3, 4) to the origin. r 4 Draw a vertical segment from (3, 4) to the x–axis. This is called the ________ ________. θ reference triangle 3 Label the sides of the right triangle. x = _____ and y = _____ 3 4

Determine r using the Pythagorean Theorem. r2 = (___)2 + (___)2 3 4 Example # 1: Determine r using the Pythagorean Theorem. r2 = (___)2 + (___)2 3 4 y x r2 = ___ 25 r = ___ 5 r = 5 4 Use an ________ trigonometric function to approximate θ. inverse θ Put your calculator in “radian” mode. 3 4 Make sure you know what mode the calculator is in! 5 3 0.93 radians 5 4 53.13 3 Now put your calculator in “degree” mode

The point (–3, 4) is on the terminal side of angle θ. Example # 2: The point (–3, 4) is on the terminal side of angle θ. Draw the ________________, and label x, y, and r. reference triangle reference angle Label the acute angle at the origin α, the _______________. This reference triangle is __________ to the reference triangle in Example # 1, so congruent y x α = ______ 53.13 r = 5 180˚ 53.13 126.87 4 = 126.87 53.13 -3

Example # 2: Since 90°< ____ < 180°, θ is a ____________ angle. Use your calculator to approximate the following: Quadrant II Check the mode, people! 126.87˚ 0.80 y x 126.87˚ r = 5 –0.60 4 = 126.87 53.13 -3 126.87˚ –1.33

In quadrant II, sinθ > _____, cosθ < ____, and tanθ < _____ Use x, y, and r on the reference triangle to find: 4 5 y x r = 5 - 3 4 = 126.87 5 53.13 -3 4 - 3

Practice: Draw angle θ in each quadrant Practice: Draw angle θ in each quadrant. Draw θ, the reference triangle, and α. QI QII QIII QIV r r θ y y θ θ x θ α –x x –x α α –y –y r r θ = α θ = 180 – α θ = 180 + α θ = 360 – α

____ ____ ____ ____ ____ ____ ____ ____ ____ No matter which quadrant θ is in, the definitions for sinθ, cosθ, and tanθ are all the same. There is a mnemonic (similar to SOH CAH TOA) to help you remember these definitions. ____ ____ ____ ____ ____ ____ ____ ____ ____ s y r c x r t y x pronounced: “Sir Kix-er Tix” y θ x

In quadrant III sinθ < ____, cosθ < _____, and tanθ > ____. Practice: The point (–3, –4) is a point on the terminal side of angle θ. Draw the reference triangle. Label the sides x, y, and r. Determine: - 4 y x ≈ 53.13˚ 5 Check the mode, people! - 3 ≈ 53.13˚ 5 θ –3 -4 4 = α -3 3 ≈ 53.13˚ –4 5 180 + α ≈ 180 + 53.13 ≈ 233.13 Note: when you are finding α you can ignore the negative signs, or just use the positive ratio (e.g. tangent in this case). In quadrant III sinθ < ____, cosθ < _____, and tanθ > ____.

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