Trig Equations Homework
Part One – Graphing Calculator Active
1. Solve the equation 3 cos x = 5 sin x, for x in the interval 0°  x  360°, giving your answers to the nearest
degree.
Part Two – Scientific Calculator only. Show all work neatly!
2.
(a) Write the expression 3 sin2 x + 4 cos x – 4 in the form a cos2 x + b cos x + c.
(b)
3.
Hence or otherwise, solve the equation
3 sin2 x + 4 cos x – 4 = 0,
0  x  90.
(a)
Factorize the expression 3 sin2 x – 11 sin x + 6.
(b)
Consider the equation 3sin2x – 11sin x + 6 = 0.
(i)
Find the two values of sin x which satisfy this equation,
(ii)
Solve the equation, for 0°  x  180°.
Part Three – NO CALCULATOR! Show all work neatly!
4.
Solve the equation 3 sin2x = cos2x, for 0°  x  180°.
5.
6.
(a)
Express 2 cos2 x + sin x in terms of sin x only.
(b)
Solve the equation 2 cos2 x + sin x = 2 for x in the interval 0  x  , giving your answers exactly.
Consider the trigonometric equation 2 sin2 x = 1 + cos x.
(a)
Write this equation in the form f(x) = 0, where f(x) = a cos2 x + b cos x + c, and a, b, c 
.
(b)
Factorize f(x).
(c)
7.
Solve f(x) = 0 for 0°  x  360°.
Solve the equation 2cos2 x = sin 2x for 0  x  π, giving your answers in terms of π.
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