y = sin x 5.5 Graphing sine and cosine functions
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1 Graphing sine and csine functins: Class ntes, G. Battaly 5.5 Graphing sine and csine functins GOALS: 1. Recgnize that f(x) = sin x and g(x) = cs x are functins. (Each value f x results in exactly 1 y value.) 2. Fr bth functins, the dmain is the set f real numbers; and the range is 1 < y < 1 3. Bth functins are peridic and repeat after a perid f 2π 4. Fr f(x) = A 1 sin x and g(x) = A 2 cs x the dmain is all real numbers, the perid is 2π, but the range is A 1 < y < A 1 and A 2 < y < A 2 respectively. 5. Fr f(x) = A 1 sinb 1 x and g(x) = A 2 csb 2 x the perid changes t 2π/B 1 and 2π/B 2, respectively, the range remains A 1 < y < A 1 and A 2 < y < A 2 respectively. 6. f(x) = A 1 sin(b 1 x C 1 )+D 1 and g(x) = A 2 cs(b 2 x C 2 )+D 2 C shifts right and left, D shifts up and dwn Study 5.5 CVC#1 5,6,9,10; # 1 9, 31 35, 39, 75, 77, 78, 85 Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 5.5 Graphing sine and csine functins y = sin x + θ θ = 0 θ = 360 sin 90 = 1 sin 0 = 0 sin 360 = 0 Cllege Algebra & Trig Hme Page θ = 90 θ = 180 θ = 270 Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY sin 180 = 0 Hmewrk sin 270 = 1 graphing ppt graphing vide G. Battaly
2 Graphing sine and csine functins: Class ntes, G. Battaly 5.5 Graphing sine and csine functins y = sin x Cllege Algebra & Trig Hme Page Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Hmewrk graphing ppt graphing vide 5.5 Graphing sine and csine functins y = cs x + θ θ = 0 θ = 360 cs 0 = 1 cs 90 = 0 cs 360 = 1 Cllege Algebra & Trig Hme Page θ = 90 θ = 180 θ = 270 cs 180 = 1 Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Hmewrk cs 270 = 0 graphing ppt graphing vide G. Battaly
3 Graphing sine and csine functins: Class ntes, G. Battaly 5.5 Graphing sine and csine functins y = cs x Try a few examples: graphing functin 1. Click n: 2. Click ff g(x) and h(x) 3. In INPUT bx, enter functins: 2. f(x) =2 cs x 6. f(x) = cs 0.5x Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk graphing ppt graphing vide 5.5 Graphing sine and csine functins a =, perid = 2π/ = graphing functin x 0 π/2 π 3π/2 2π sin x Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x G. Battaly
4 Graphing sine and csine functins: Class ntes, G. Battaly 5.5 Graphing sine and csine functins a = 1, perid = 2π/1 = 2π graphing functin x sin x 0 0 π/2 1 π 0 3π/2 1 2π 0 a = 1 perid = 2π Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x 5.5 Graphing sine and csine functins 2. f(x) =2 cs x a =, perid = 2π/ = x cs x 2 cs x 0 1 π/2 π 1 3π/ π graphing functin Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x G. Battaly
5 Graphing sine and csine functins: Class ntes, G. Battaly 5.5 Graphing sine and csine functins 2. f(x) =2 cs x a = 2, perid = 2π/1 = 2π x cs x 2 cs x π/2 0 0 π 1 2 3π/ π 1 2 graphing functin a = 2 perid = 2π Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x 5.5 Graphing sine and csine functins a = 0.5, perid = 2π/1 = 2π x sin x 0.5sinx =1 π/2 1 π 0 3π/2 1 2π 0 graphing functin Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x G. Battaly
6 Graphing sine and csine functins: Class ntes, G. Battaly 5.5 Graphing sine and csine functins a = 0.5, perid = 2π/1 = 2π x sin x 0.5sinx =1 π/ =1.5 π 0 0+1=1 3π/ =0.5 2π 0 0+1=1 graphing functin a = 0.5 perid = 2π Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x 5.5 Graphing sine and csine functins a = 1, perid = 2π/2 = π x 2x sin2x π/2 π 0 π 2π 0 3π/2 3π 0 2π 4π 0 π/4 3π/4 3π/2 need between values graphing functin Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x G. Battaly
7 Graphing sine and csine functins: Class ntes, G. Battaly 5.5 Graphing sine and csine functins a = 1, perid = 2π/2 = π x 2x sin2x π/2 π 0 π 2π 0 3π/2 3π 0 2π 4π 0 π/4 π/2 1 3π/4 3π/2 1 need between values (π/4,1) graphing functin a = 1 (3π/4, 1) perid = π Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x 5.5 Graphing sine and csine functins a = 3, perid = 2π/1 = 2π graphing functin x 0 π/2 π 3π/2 2π sin x 3sin x Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x G. Battaly
8 Graphing sine and csine functins: Class ntes, G. Battaly 5.5 Graphing sine and csine functins a = 3, perid = 2π/1 = 2π graphing functin x sin x 3sin x π/2 1 3 π 0 0 3π/ π 0 0 a = 3 perid = 2π Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Cllege Algebra & Trig Hme Page Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x 5.5 Graphing sine and csine functins 6. f(x) = cs 0.5x a = 1, perid = 2π/0.5 = 4π x 0.5x cs 0.5x 0 0 π π/2 2π 3π 3π/2 4π graphing functin Cllege Algebra & Trig Hme Page Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x G. Battaly
9 Graphing sine and csine functins: Class ntes, G. Battaly 5.5 Graphing sine and csine functins 6. f(x) = cs 0.5x a = 1, perid = 2π/0.5 = 4π graphing functin x 0.5x cs 0.5x π π/2 0 2π π 1 3π 3π/2 0 4π 2π 1 1/2 cycle a = 1 perid = 4π Cllege Algebra & Trig Hme Page Class Ntes: Prf. G. Battaly, Westchester Cmmunity Cllege, NY Hmewrk 2. f(x) =2 cs x 6. f(x) = cs 0.5x G. Battaly
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