Download Chapter 13 Review Problems

Chapter 13 Review Problems IB Math AP Carandang
1.
If A is an obtuse angle in a triangle and sin A = 5 , calculate the exact value of sin 2A.
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2.
(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.
(a)
Factorize the expression 3 sin2 x – 11 sin x + 6.
(b)
Consider the equation 3 sin2 x – 11 sin x + 6 = 0.
3.
4.
(i)
Find the two values of sin x which satisfy this equation,
(ii)
Solve the equation, for 0°  x  180°.
(a)
Write the expression 3 sin2 x + 4 cos x in the form a cos2 x + b cos x + c.
(b)
Hence or otherwise, solve the equation
3 sin2 x + 4 cos x – 4 = 0,
0  x  90.
5.
Find all solutions of the equation cos 3x = cos (0.5x), for 0  x  .
6.
Given that sin x =
7.
(a)
cos x;
(b)
cos 2x.
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, where x is an acute angle, find the exact value of
3
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)
Solve f (x) = 0 for 0°  x  360°.
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8.
Solve the equation 3 cos x = 5 sin x, for x in the interval 0°  x  360°, giving your answers to
the nearest degree.
9.
Solve the equation 3 sin2 x = cos2 x, for 0°  x  180°.
10.
Solve the equation 2 cos2 x = sin 2x for 0  x  π, giving your answers in terms of π.
11.
The following diagram shows a triangle ABC, where AĈB is 90, AB = 3, AC = 2 and BÂC
is .
12.
(a)
Show that sin  =
5
.
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(b)
Show that sin 2 =
4 5
.
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(c)
Find the exact value of cos 2.
The function f is defined by f : x  30 sin 3x cos 3x, 0  x 
π
.
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(a)
Write down an expression for f (x) in the form a sin 6x, where a is an integer.
(b)
Solve f (x) = 0, giving your answers in terms of .
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