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4.3A Trigonometric Ratios

Learn how to find the exact values of the six trigonometric ratios for a point P(x, y) on the terminal arm of an angle in standard position that intersects the unit circle.

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4.3A Trigonometric Ratios

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  1. 4.3A Trigonometric Ratios r = √x2 + y2 Point P(x, y) is the point on the terminal arm of angle  ,an angle in standard position, that intersects a circle. P(x, y) r2 = x2 + y2 r y q x The three reciprocal ratios are defined as follows: Math 30-1

  2. Finding the Trig Ratios of an Angle in Standard Position The point P(-2, 3) is on the terminal arm of qin standard position. No, the radius of a unit circle is 1. Does point P(-2, 3) lie on the unit circle? Determine the exact value of the six trigonometric ratios for angle q. P(-2, 3) 3 q -2 r2 = x2 + y2 r2= (-2)2 + (3)2 r2= 4 + 9 r2= 13 r = √ 13 Math 30-1

  3. 4.2 Trig Ratios McGraw Hill DVD Teacher Resources 4.2193IA is a point on the terminal arm of angle θ that intersects the unit circle Math 30-1

  4. The point lies at the intersection of the unit circle and the terminal arm of an angle θin standard position. Diagram q r = 1 Math 30-1

  5. (0, 1) (1, 0) (-1, 0) (0, -1) The Unit Circle Exact Values for the trigonometric ratios can be determined using multiples of special angles for points P(θ) on the unit circle. Math 30-1

  6. Exact Values For Trigonometric Ratios 2. cos 1. sin 3300 = RA = 300 quadrant IV RA = quadrant II 3. tan 4. cos= RA = quadrant IV RA = quadrant III Math 30-1

  7. Using the unit circle Determine the exact value of: Math 30-1

  8. Approximate Values for Trig Ratios (four decimal places) 1. sin 250 = 2. cos3750 = 3. 4. csc 1.57= 5. 6. cot 2700= The mode of calculator must match the domain of the angle, degrees or radians. Math 30-1

  9. Assignment Exact Values of Trig Ratios given an angle or P(x,y) Page 201 1, 2, 3, 6, 7, 8, 13 Math 30-1

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