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Form 4 mathematics trigonometry III questions and answers
Given that sin (x +
30
0
) = cos 2x for
0
0
≤ x≤
90
0
find the value of x.
Hence find the value of
cos
2
3x.
(2m 45s)
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1.
Solve the equation:Sin (
1
2
x
-
30
0
) = cos x for 0 < x <
90
0
2.
Solve for x: 4 sin
(
x
+
20
)
0
=3 for
0
0
= x =
360
0
3.
Solve the equation;sin
5
2
θ
=
1
2
for
0
0
=
θ
=
180
0
4.
Solve for
θ
in the equation:
sin
(
2
θ
–
= -0.5 for
0^0 = theta = 360^0
5.
Determine the amplitude and the period for the graph of y =6 sin
{ x/2 - 90}^0
6.
Find all the values of
theta
between
0^0
and
360^0
satisfying the equation 5 sin
theta
= -4.
7.
Solve the equation;cos
(3theta+120^0)=frac{sqrt3}{2}
For
0^0 = theta = 180^0
8.
Solve the equation:
8s^2 + 2s -3 =0
Hence solve the equation:
8sin^2theta +2sintheta-3=0
For
0^0 = theta = 180^0
9.
Solve the equation:
2sin^2
(x -
30^0
) = cos
60^0
For -
180^0 = x= 180^0
10.
Given that sin (x +
30^0
) = cos 2x for
0^0
= x=
90^0
find the value of x. Hence find the value of
cos^2
3x.
11.
Solve the equation:
4Sin^2theta
+
4 Cos theta
= 5 for
0^0 = theta = 360^0
.Give the answer in degrees.
12.
Solve the equation:
3tan^2
x – 4 tan x – 4 =0. For
0^0 = x = 180^0
.
13.
Given that
x^0
is an angle in the first quadrant such that 8
sin^2x
+2cosx -5 =0 find; a) cos x b).tan x.
14.
Given that Cos 2x = 0.8070, find x when
0^0 = x = 180^0
15.
Solve the equation 3cos x =
2sin^2x
where
0^0= x = 360^0
16.
Solve the equation: 2
cos2theta
= 1 For
0^0= theta = 360^0
17.
Solve the equation: Sin
(3x+30)^0
=
frac{sqrt3}{ 2}
,for For
0^0 = x = 90^0
18.
Solve:4 – 4
cos^2alpha
= 4sin
alpha
-1 For
0^0 = alpha = 360^0
19.
Solve the equation: Sin
(2t +10)^0
=0.5 for
0^0= t = 180^0
20.
Given that sin
(x+20)^0
= -0.7660, find x to the nearest degree, for
0^0= x = 360^0
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