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Homework: Graphs & Trig Equations

Homework: Graphs & Trig Equations. State the amplitude, period & then sketch the graph of (a) y = 3 cos 5x + 1 0 ≤ x ≤ 90 (b) y = ½ sin 2x 0 ≤ x ≤ 360. Homework: Graphs & Trig Equations. 3. 72 o. Max = c + a Max = 1 + 3 = 4 Min = c – a Min = 1 – 3 = -2 . 4.

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Homework: Graphs & Trig Equations

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  1. Homework: Graphs & Trig Equations State the amplitude, period & then sketch the graph of (a) y = 3 cos 5x + 1 0 ≤ x ≤ 90 (b) y = ½ sin 2x 0 ≤ x ≤ 360

  2. Homework: Graphs & Trig Equations 3 72o Max = c + a Max = 1 + 3 = 4 Min = c – a Min = 1 – 3 = -2 4 (a) y = 3 cos 5x + 1 0 ≤ x ≤ 90 Amplitude, a = , Period = 360= 5 1 18 36 54 72 90 -2

  3. Homework: Graphs & Trig Equations 180o ½ Max = c + a Max = 0 + ½ = ½ Min = c – a Min = 0 – ½ = – ½ ½ (b) y = ½ sin 2x 0 ≤ x ≤ 360 Amplitude, a = , Period = 360= 2 0 45 90 135 180 225 270 315 360 -½

  4. Homework: Graphs & Trig Equations y = a cos (bx) + c 2(a) Amplitude = 5 – (-3) = 8 = 4 Period = 180o 2 2 (2 graphs in 360) Max = c + a 5 = c + 4 C = 1 y = 4cos (2x) + c y = 4 cos (2x) + 1

  5. Homework: Graphs & Trig Equations y = a cos (bx) + c 2(b) Amplitude = 1 – (-1) = 2 = 1 Period = 720o 2 2 (½ graph in 360) Max = c + a 1 = c + 1 C = 0 y = 1cos (½x) + c y = cos ( ½ x)

  6. Homework: Graphs & Trig Equations y = tan (bx) + c 2(b) Amplitude = doesn’t exist Period = π/4 (1 rep in π/4 rather than 1 in π b = 4) Normally starts at (0,0) so pushed up 1 position  c = 1 y = tan (4x) + c y = tan (4x) + 1

  7. Homework: Graphs & Trig Equations = - Sin 45 = tan π/6 = - Cos 30 = - √3 2 = - 1 √2 = 1 √3 5(a) Sin 315 (b) tan 7π/6 (c) Cos(-150)

  8. Homework: Graphs & Trig Equations = (- Cos 30)2– (sin 30)2 = sin (π/3) x-sin (π/4) = (-√3/2)2 – ( ½ )2 = √3 x-1 2 √2 = 3 – 1 4 4 6(a) cos2210 – sin230 (b) sin (π/3) sin (5π/4) = -√3 2√2 = 1 2

  9. Homework: Graphs & Trig Equations = 1 – 2 x(- Sin 60)2 = 1 – 2 x (-√3/2)2 = 1 – 2 x (3/4) 6(c) 1 – 2 sin2300 = 1 – 3/2 = - ½

  10.  S A Homework: Graphs & Trig Equations 1st Quadrant:3x = Sin-1(0.32) T C 3x = 18.7 2nd Quadrant: 3x = 180 – 18.7 = 161.3 9(a) Sin 3x = 0.32 0 ≤ x ≤ 90 Remember you must change the range: 0 ≤ x ≤ 90 0 ≤ 3x ≤ 270 3x = 18.7 ; 161.3 x = 6.2 ; 53.8

  11. 3Cos(4t – 30) = 3  Cos(4t – 30) = 1 S A Homework: Graphs & Trig Equations 1st Quad:(4t – 30) = Cos-1(1) = 0 T C  4th Quad: 360 – 0 = 360 Remember the range: 0 ≤ t ≤ 90 (4(0) – 30) ≤ (4t – 30) ≤ (4(90) – 30) – 30 ≤ (4t – 30) ≤ 330 9(c) 2 + 3Cos(4t – 30) = 5 0 ≤ t ≤ 90 (4t – 30) = 0, 360 4t = 30 t = 7.5

  12. Sin2 x = ¼   Sin x = ± ½ S A Homework: Graphs & Trig Equations 1st Quad:x = Sin -1( ½ ) = π/6 T C   ** As both signs  in all 4 quadrants 2nd Quad:π – π/6 = 5π/6 9(e) 4 Sin2 x = 1 0 ≤ x ≤ 2π 3rd Quad:π + π/6 = 7π/6 4th Quad: 2π – π/6 = 11π/6 x = π/6 ; 5π/6 ; 7π/6 ; 11π/6

  13. (2Cost – 1)(Cost – 1) = 0   S A S A Homework: Graphs & Trig Equations T C T C   2Cost – 1 = 0 Cost – 1 = 0 Cost = ½ Cost = 1 1stQuad: t = Cos -1( ½ ) = 60 1st Quad: t = Cos -1( 1 ) = 0 9(g) 2Cos2 t – 3Cos t + 1 = 0 0 ≤ t ≤ 360 4th Quad: 360 – 60 = 300 4thQuad: 360 – 0 = 360 t = 0 ; 60 ; 300 ; 360

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