Cos 2x sin x
[DOC File]CHAPTER 10 : TRIGONOMETRIC FUNCTIONS, IDENTITIES & …
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Prove that sin x cos x – sin2 x - can be expressed as cos (2x - ) – 1. With the help of the curve of y = cos 2x, sketch, for values of x such that 0 ( x ( (, the graph of y = sin x cos x – sin2 x + .
Amplitude and Period for Sine and Cosine Functions Worksheet
Determine the amplitude, period, phase shift, and vertical shift for each. 1.y = 2 sin 3x2.y = sin (x − π) 3.y = 3 cos 4x4.y = 3 sin 6x − 3
[DOC File]Amplitude and Period for Sine and Cosine Functions Worksheet
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Sketch the graph of the function over the interval –2( ≤ x ≤ 2(. 11. y = 4 sin x 12. y = 2 cos x. 13. y = 2 sin 2x 14. y = – cos 2x 15. y = 3 cos x 16. y = – 2 sin (4x) Determine the amplitude, period, phase shift, and vertical shift for each. 17. 18. y = 2 cos (x − π) 19. 20. Sketch the graph of each function for . …
[DOC File]SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS
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yh = e–x (c1 sin 2x + c2 cos 2x) Since the nonhomogeneous term r(x) contains terms of ex and sin 2x, we can assume the particular solution of the form. yp = c ex + m sin 2x + n cos 2x. After substitution the above yp into the nonhomogeneous equation, we arrive.
[DOCX File]Solve each trigonometric equation for x where
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Solve each trigonometric equation or inequality for x where . 0≤x
[DOC File]C3 Trigonometry
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sin x + (3 cos x = 2 sin 2x. (3) (c) Deduce from parts (a) and (b) that sec x + (3 cosec x = 4 can be written in the form sin 2x – sin (x + 60() = 0. (1) 3. (i) (a) Express (12 cos ( – 5 sin in the form R cos (( + (), where R > 0 and 0 < ( < 90(. (4) (b) Hence solve the equation. 12 cos ( – 5 sin ( = 4, ...
[DOC File]Ex
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5. 6. Ex. Differentiate f (x) = sin(x + sin 2x) f ′(x) = cos(x + sin 2x)∙ (x + sin 2x)′ = cos(x + sin 2x)∙(1 + 2 cos 2x) = (1 + 2 cos 2x) cos(x + sin 2x) Ex. Given values of f , g, f ′, and g′ : x f(x) g(x) f ′(x) g′(x) 1 3 2 4 6 2 1 8 5 7 3 7 2 7 9 (a) If h(x) = f (g(x)), find h′(1). ...
[DOC File]Paper Reference(s)
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(a) Express 3 sin x + 2 cos x in the form R sin (x + α) where R > 0 and 0 < α < . (4) (b) Hence find the greatest value of (3 sin x + 2 cos x)4. (2) (c) Solve, for 0 < x < 2π, the equation 3 sin x + 2 cos x = 1, giving your answers to 3 decimal places. (5) June 2007. 7. (a) Express 4 cosec2 2θ − cosec2 θ in terms of sin θ and cos θ. (2)
[DOC File]Trigonometry Review
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a) cos b) sin c) tan d) cos e) sin f) cos . 8. Solve for. a) cos2 b) 2sin2x + sin x – 1 = 0 c) 10cos2(2x) + 7cos(2x) = 6. d) 4cos2(2x) – 1 = 0 e) 3tan2x = 1 f) 2tan2x + tan x – 3 = 0. g) 6cos2x – sin x – 4 = 0 h) 2cos x = 1 – sin2 x i) 2sin2 x = -cos x + 1. 9.
[DOC File]Amplitude and Period for Sine and Cosine Functions Worksheet
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Sketch the graph of the function over the interval –2( ≤ x ≤ 2(. 11. y = 4 sin x 12. y = 2 cos x. 13. y = 2 sin 2x 14. y = – cos 2x 15. y = 3 cos x 16. y = – 2 sin (4x) Determine the amplitude, period, phase shift, and vertical shift for each. 17. 18. y = 2 cos (x − π) Amplitude _____ Amplitude _____
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