Question

Question 2 2.1 2.2 2.2.1 2.2.2 Determine the general solution for sin(x - 30°) = cos 2x Consider the functions f(x) = sin(x-30°) and g(x) = cos 2x Write down the period of g. State the range of f.​

Answer 1

The general solution for the given equation is 40°+120°n.

The period of g(x) is π.

The range of f(x) is [-1, 1].

• sin(x-30°) = cos 2x
• sin(x-30°) = sin(90°-2x)
• (x-30°) = (90°-2x) + 360°n
• x + 2x =  90° + 30° + 360°n
• 3x = 120° + 360°n
• x = (120° + 360°n)/3
• The general solution (x) is 40° + 120°n.

• g(x) = cos 2x
• The period of cos x is 2π.
• If the multiplying factor of x is 'n', then it decreases the period by n times.
• Here, in g(x), n is 2.
• The period of g(x) is equal to half the period of cos x.
• The period of g(x) = 2π/2
• The period of g(x) is π.

• f(x) = sin(x-30°)
• "Sin" is a trigonometric function which has a range from -1 to 1.

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