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1.3

1.3. Right Triangle Trigonometry. Unit Circle Definitions of the 6 Trig. Functions…. sin = y. cos = x. y x. 1 x. x y. 1 y. tan =. csc =. sec =. cot =. Non-Unit Circle Definitions of the 6 Trig. Functions…. y r. sin =. x r. cos =. y x. r x. x y. r y. tan =.

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1.3

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  1. 1.3 Right Triangle Trigonometry

  2. Unit Circle Definitions of the 6 Trig. Functions… sin = y cos = x y x 1 x x y 1 y tan = csc = sec = cot =

  3. Non-Unit Circle Definitions of the 6 Trig. Functions… y r sin = x r cos = y x r x x y r y tan = csc = sec = cot =

  4. These definitions are closely related to the unit circle definition. In the unit circle, the radius is = to 1, thereby eliminating the denominator. y r sin = x r cos =

  5. Since this is a unit circle (radius of one), sin 45 = 2/2 (0,1)  (2, 2) (2/2, 2/2) Now, on this second circle, the radius is no longer 1 unit (it’s 2). Therefore, sin 45 = y/r or sin 45 = 2/2 (2,0) (-1,0)  (1,0) 45  (0,-1)

  6. Let’s practice these definitions. Find exact values of the six trig. functions of the angle  shown in the figure. = = = = = = 12 5 13 12 13 5 5 13 12 13 5 12 If this triangle was placed at the center of a circle, what would the radius of that circle be? sin  = cos = tan  = cos = cot  = csc = y x r y x r r x x y y r (12,5)  13 5  a2 +b2 = c2 12 122 +52 = c2 169 = c2 13 = c

  7. Your Turn #1: Place your work in your notebook. Find exact values of the six trig. functions of the angle  shown in the figure. 5  5 Look back at the previous slide if you need assistance.

  8. Your Turn #2: Place your work in your notebook. Find exact values of the six trig. functions of the angle  shown in the figure. 4  8 Hint: Be sure to reduce radicals.

  9. Let’s practice some more… Sketch a right triangle corresponding to the trig. function of the acute angle . Then determine the other five trig. functions of . = = = = = = 25 5 35 5 y r 3 2 5 3 5 2 tan  = sec  = csc = cos = cot  = y x r x x y x r r y (5,2)  3 sin  = 2 3  2 5 a2 + b2 = c2 a2 + 22 = 32 a2 + 4 = 9 a2 = 5 a = 5

  10. Your Turn #3: Place your work in your notebook. Sketch a right triangle corresponding to the trig. function of the acute angle . Then determine the other five trig. functions of . Think sec  = 4/1 sec  = 4 Look back at the previous slide if you need assistance.

  11. Your Turn #4: Place your work in your notebook. Sketch a right triangle corresponding to the trig. function of the acute angle . Then determine the other five trig. functions of . csc = 9 5 Look back if you need assistance.

  12. What is SOH CAH TOA? This is another way of remembering the definitions of the trigonometric functions. SOH sin = opposite hypotenuse Hyp. Opp. 

  13. What is SOH CAH TOA? CAH cos = adjacent hypotenuse Hyp.  Adj.

  14. What is SOH CAH TOA? TOA tan = opposite adjacent Opp.  Adj.

  15. Assignment: pg. 156: 1-26

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