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3.5 The Trig Functions

3.5 The Trig Functions. sine and cosine are only 2 of the trig functions! Here are all 6!. cosecant. sine. , y ≠ 0. cosine. secant. , x ≠ 0. cotangent. tangent. , y ≠ 0. , x ≠ 0.

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3.5 The Trig Functions

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  1. 3.5 The Trig Functions

  2. sine and cosine are only 2 of the trig functions! Here are all 6! cosecant sine , y≠ 0 cosine secant , x≠ 0 cotangent tangent , y≠ 0 , x≠ 0

  3. Ex 1) The terminal side of an angle θ in standard position passes through (–1, 7). Draw the reference triangle and evaluate the six trig functions of θ. 72 + (–1)2 = r2 50 = r2 r 7 θ  r always (+) –1

  4. A relationship among the 6 trig functions is they can pair up & make pairs of reciprocal functions. (as always den ≠ 0) Ex 2) Determine the value of secθ if cosθ = 0.11

  5. If we know the value of one trig function & the quadrant of θ, we can get the other 5 Ex 3) Angle in standard position, Quadrant IV and x θ –6 7

  6. Ex 4) Suppose that cosθ = 0.42 and Use the symmetry of the unit circle to find the exact values of the following. a) cos(–θ) b) cos(θ + π) c) cos(θ + 2π) + π + 2π θ θ θ –θ x-value is the same so cos(–θ) = 0.42 x-value is negative so cos(θ + π) = –0.42 right where you started so cos(θ + 2π) = 0.42

  7. Homework #305 Pg 150 #1, 5, 9, 13, 15, 17, 21, 26, 27, 29, 31, 33, 37, 43, 44, 45, 46

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