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# L09_blanks - Day 10 Lecture 09 for Generalizing...

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1 Day 10 Lecture 09 for 2/08/2011 Generalizing Trigonometry, part Tres More Generalizations If a point ( x,y ) in the plane is on the unit circle then that points’ coordinates give the values of the trigonometric functions for any angle whose terminal side goes through that point. But what if the point is not on the unit circle? In that case, we can normalize the point by dividing its ______________ by the point’s norm , r, its _______________ from the origin. Slide: 2of 16 is 0

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2 Trig. Functions defined by Normalized Pts. Let ( x , y ) be a point in space. Let r = Then, Notice : 1) From the last slide we know ___________ is a point on the unit circle. 2) This definition of the 6 trig. functions agrees with the unit circle definition when r = ___ 3) And agrees with the right triangle definition if the point ( x , y ) is in quadrant ___ . 4) If x = 0 , secant and tangent are _____________. 5) If y = 0 , cosecant and cotangent are _____________. Slide: 3of 16 is 0 Evaluating the Trig functions for Any Point The point lies on the terminal ray of the angle in standard position.
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L09_blanks - Day 10 Lecture 09 for Generalizing...

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