Trigonometric functions

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The Trigonometric  functions are also called “the circular functions” comprising trigonometry: the cosecant is called cscx, cosine is called cosx, cotangent is called cotx, secant is called secx, sine is called sinx, and tangent is called tanx in trigonometric functionsHowever, their other notations are used occasionally. Their values with theta and functional values mentioned below: 

Formulae:
  • Sin 2θ = 2 sin θ cos θ
  • Cos 2θ = cos²θ - sin²θ
  • cos² θ2 = (1+cosθ)2
  • sin² θ2 = (1-cosθ)2
Example 1: Simplify 2 cosx cos2x sin3x – 2 sinx sin2x sin3x
(a) sin 4x          (b) cos 4x           (c) sin 6x          (d) cos 6x
Answer: (c) sin 6x
Explanation: 2 cosx cos 2x sin 3x – 2 sinx sin 2x sin 3x
= 2 sin3x (cos x cos 2x – sin x sin 2x)
= 2 sin 3x (cos (x+2x))
= 2 sin 3x cos 3x
= sin 6x
 
Example 2: sec² x – 3sec x +2 = 0, 0 ≤ x ≤ 2π. Solve for x
Answer: Let sec x = y
y² - 3y + 2 = 0
(y – 1) (y -2 ) = 0
y=1 or y = 2
sec x = 1 or sec x = 2
x = 0° or 60°

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