THE WAVE FUNCTION
3 sin x° - cos x° in the form k sin(x – a)° where k > 0 and 0° ≤ a < 360°
1C)
Express
2C)
Express 8cos x° - 6sin x° in the form k cos(x + a)° where k > 0 and 0° < a < 360°
3C)
Express 8sin x - 5cos x in the form k sin(x + a)° where k > 0 and 0 ≤ a ≤ 2π
4C)
Prove the
5C)
The voltage, V volts, necessary to produce
a certain alternating current at time t in milliseconds (t > 0) can be expressed in the form:
V = 2sin 300t° + 3cos 300t°

3 cos x  sin x  2cos( x  )
6
Express V in the form ksin(300t + θ)° where 0 ≤ θ ≤ 180°.
(i) Find the maximum value of V.
(ii) Find the first time that the voltage reaches 2 volts.
a)
b)
6C)
Part of the graph y = 2sin x° + 5cos x° is shown in the diagram.
y
360
P
x
•
a) Express y in the form k sin (x + a)° where k > 0 and 0° < a < 360°
b) Find the coordinates of the minimum turning point P.
7C)
Find the maximum value of cos x – sin x and the value of x for which it occurs in
the interval 0 ≤ x ≤ 2π.
8)
k and α are given by ksinα = 4 and kcosα = -1 where 0 ≤ α ≤  . The value of k
and the range of values for α are
A.
B.
C.
D.
9)
k and α are given by ksinα = -1 and kcosα = 3 where 0 ≤ α ≤ 2  . The value of k
and the range of values for α are
A.
B.
C.
D.
10)
2
3
√24 and tanα = 5
√24 and tanα = 1 5
√26 and tanα = -5
√26 and tanα = - 1 5
2 and 150°
2 and 120°
√10and 150°
√10 and 120°
The maximum value of 1 - (4sinx - 3cosx) is
A.
B.
C.
D.
13)
<α< 
2 < α < 2
 <α< 
2
3
2 < α < 2

Given that ksinα° = √3 and kcosα° = -1, the values of k (k > 0) and α (0° ≤ α ≤
360°) are
A.
B.
C.
D.
12)
√10 and
√10 and
2√2 and
2√2 and
When 5cosx - sinx is expressed in the form ksin(x + α), the value of k and tanα are
A.
B.
C.
D.
11)
√17 and  2 < α < 
√17 and 0 < α <  2
√15 and  2 < α < 
√15 and 0 < α <  2
8
-6
0
6
When 3sinx + cosx is expressed in the form kcos(x - a), the value of k and the
range of values for a when k > 0 and 0 ≤ a ≤  are
A.
B.
C.
D.
k = 2 and  2 ≤ a ≤ 
k = √10 and  2 ≤ a ≤ 
k = 2 and 0 ≤ a ≤  2
k = √10 and 0 ≤ a ≤  2