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pencil, red pen, highlighter, calculator, notebook
U8D5 Have out: pencil, red pen, highlighter, calculator, notebook Bellwork: 1. Convert each degree to radians. a) 280o +2 b) -330o +2 2. Convert each radian to degrees. a) = 144o +2 b) = –40o +2 3. Determine the lengths of all sides. Give the exact answers! a) b) 30° 1 60° 45° 1 total:
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Bellwork: 3. Determine the lengths of all sides. Give the exact answers! a) b) 30° 1 60° 45° 1 30° – 60° – 90° SL: n = LL: n = Hyp: 2n = +1 45° – 45° – 90° leg: n = Hyp: = +1 +1 +1 +1 +1 1 u +1 1 u +1 +1 +1 work total:
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COTERMINAL angles share their terminal side.
120° x For example, 120° is coterminal with –240°. –240° What else is coterminal with 120o? 120o 480o 840o + 360o + 360o + 360o 480o 840o 1200o See a pattern? Just spin around the circle by adding (or subtracting) 360o.
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Practice #1: For each angle,
(i) Draw a sketch. (ii) Find a coterminal angle, and show it in the sketch. Remember: _________________ add or subtract 360. 1) 2) 3) y y y 30o x x x –80o –260o 100o –330o 280o –360o +360o –360o –260o 30o –80o or 640o or 460o or –690o
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Practice #1: For each angle,
(i) Draw a sketch. (ii) Find a coterminal angle, and show it in the sketch. 4) 5) 6) y y y 320o 180o x x x –216o –40o –180o 144o +360o +360o –360o 320o 180o –216o or –540o or 504o –400o
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Practice #2: For each angle,
(i) Draw a sketch. (ii) Find a coterminal angle, and show it in the sketch. Remember: _________________ add or subtract 2π. 2) 3) 1) y y y x x x
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Practice #3: For each sketch, determine θ
Practice #3: For each sketch, determine θ. (Make sure your calculator is in degree mode!) y y 1) 2) 5 5 Chose the trig ratio with the positive fraction x x 4 -3
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Practice #3: For each sketch, determine θ
Practice #3: For each sketch, determine θ. (Make sure your calculator is in degree mode!) y y 3) 4) –4 x 6 x –7 –3
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Practice #4: Determine in which quadrant each angle lies
Practice #4: Determine in which quadrant each angle lies. Then find sinθ, cosθ, and tanθ. (Use your calculator!) 1) θ = 134° Quadrant: ____ sinθ = _____ cosθ = _____ tanθ = _____ 2) θ = 85° Quadrant: ____ sinθ = _____ cosθ = _____ tanθ = _____ Conclusion: Which ones are positive in each quadrant? For example, all of them are positive in Quadrant I. Label the rest. II I 0.72 0.996 -0.69 0.09 -1.04 11.43 y ALL ______ x II III IV I 3) θ = 250° Quadrant: ____ sinθ = _____ cosθ = _____ tanθ = _____ 4) θ = 317° Quadrant: ____ sinθ = _____ cosθ = _____ tanθ = _____ III IV -0.94 -0.68 -0.34 0.73 2.75 -0.93
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Let’s come up with a method for remembering this.
y ALL ______ x II III IV I Let’s come up with a method for remembering this. Base it on this: A S T C What words can we use to remember this?
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Practice #5: The given point is on the terminal side of θ.
Complete the following: Example: (3, –4) Plot the point. Show θ and α. Draw the reference triangle Label x, y, and r. Determine sinθ, cosθ, and tanθ. Approximate θ. y x = 3 x y = –4 r = 5 Pythagorean Triplet: 3, 4, 5
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Practice #5: The given point is on the terminal side of θ.
Complete the following: Example: (3, –4) (v) Determine sinθ, cosθ, and tanθ. y x = 3 x (vi) Approximate θ. y = –4 Why use cosine? r = 5 It’s positive in quadrant IV.
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Unit Circle Quiz tomorrow!
Complete the rest of the worksheets. Reminder: Unit Circle Quiz tomorrow!
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