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(x, y) r Use Pythagorean Theorem: x 2 + y 2 = r 2 Note: x can be  and y can be  (depending on the Quadrant) Since r is the radius, it must be (+) because.

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Presentation on theme: "(x, y) r Use Pythagorean Theorem: x 2 + y 2 = r 2 Note: x can be  and y can be  (depending on the Quadrant) Since r is the radius, it must be (+) because."— Presentation transcript:

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2 (x, y) r Use Pythagorean Theorem: x 2 + y 2 = r 2 Note: x can be  and y can be  (depending on the Quadrant) Since r is the radius, it must be (+) because it is a length.  ’’ A reference angle,  ’, is the smallest, positive degree measure from the terminal side to the x-axis.

3 y y x x r r Cosine: Sine: Tangent: Secant: Cosecant: Cotangent: cos  = x sin  = y tan  = y sec  = r csc  = r cot  = x

4 If the terminal ray of angle  in standard position contains (x, y) on the unit circle, then cos  = x and sin  = y or (cos , sin  ) = (x, y). -1 ≤ cos  ≤ 1 and -1 ≤ sin  ≤ 1 Look at x-values and y- values so far on the unit circle b/c radius is always 1

5 A. Finding trig values using calculator: Use a calculator. Round to the nearest four decimal places. a) Sin 45°  sin 45 enter NOTE: Make sure your calculator is in degree mode. b) cos 20°  cos 20 enter

6 entercos entersin B. Finding angles using trig values and a calculator: If 0  <  < 90 , what is  ? Round angles to the nearest tenth. a) sin   NOTE: Make sure your calculator is in degree mode. b) cos   nd You’re “undoing” sine  = 32.0  2nd  = 43.8 

7 sin  cos  = sin  cos  y y x x r r Cosine: Sine: Tangent: Secant: Cosecant: Cotangent: cos  = x sin  = y tan  = y sec  = r csc  = r cot  = x = cos  = 1

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