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We know the trig ratios:

Lets apply trig ratios to the circle. We are going to start with a very general rule and progress into more specifics over the next week or so. We know the trig ratios: For example sin = opp./ hyp . and cos = adj./ hyp and tan = opp./ hyp.

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We know the trig ratios:

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  1. Lets apply trig ratios to the circle. We are going to start with a very general rule and progress into more specifics over the next week or so. We know the trig ratios: For example sin = opp./hyp. and cos = adj./hyp and tan = opp./hyp. What does this look like on a circle graph? I know what does a circle have to do with triangles! Lets take a look and see.

  2. Now lets add a circle through the point and with the origin as its center. Lets start with a point. P(x,y) r What does a point really mean well it means that it is x units left or right from the origin and y units up or down from the origin. Y X What is true about the hypotenuse of the triangle and the radius of the circle? Therefore we can find the trig ratios of any point from the origin (reference angle) just by its x and y. Sin = y/r Cos = x/r Tan = y/x Bingo they are the same so we can say the hypotenuse is r.

  3. Lets try it with an actual point. Now lets add a circle through the point and with the origin as its center. Lets start with a point. P(3,4) 5 What does a point really mean well it means that it is x units left or right from the origin and y units up or down from the origin. 4 3 What is true about the hypotenuse of the triangle and the radius of the circle? Therefore we can find the trig ratios of any point from the origin (reference angle) just by its x and y. Sin = 4/5 Cos = 3/5 Tan = 4/3 Using Pythagorean theorem we find that the radius is 5.

  4. Lets try it with an actual point. Now lets add a circle through the point and with the origin as its center. Lets start with a point. P(1,2) √5 What does a point really mean well it means that it is x units left or right from the origin and y units up or down from the origin. 2 1 Therefore we can find the trig ratios of any point from the origin (reference angle) just by its x and y. What is true about the hypotenuse of the triangle and the radius of the circle? Using Pythagorean theorem we find that the radius is √5.

  5. Assignment: Draw the circle with the given points find the radius and the trig ratios sin,cos, and tan. 1.) (8,6) 2.) (3,2) 3.) (5,√11) 4.) (1,1) 5.) (√2,4) 6.) (3,6)

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