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Form 4 mathematics trigonometry III questions and answers
Given that
x
0
is an angle in the first quadrant such that 8
sin
2
x
+2cosx -5 =0 find;
a) cos x
b).tan x.
(7m 21s)
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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
–
10
0
)
= -0.5 for
0
0
=
θ
=
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
θ
between
0
0
and
360
0
satisfying the equation 5 sin
θ
= -4.
7.
Solve the equation;cos
(
3
θ
+
120
0
)
=
√
3
2
For
0
0
=
θ
=
180
0
8.
Solve the equation:
8
s
2
+
2
s
-
3
=
0
Hence solve the equation:
8
sin
2
θ
+
2
sin
θ
-
3
=
0
For
0
0
=
θ
=
180
0
9.
Solve the equation:
2
sin
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:
4
sin
2
θ
+
4
cos
θ
= 5 for
0
0
=
θ
=
360
0
.Give the answer in degrees.
12.
Solve the equation:
3
tan
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
2
x
+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 =
2
sin
2
x
where
0
0
=
x
=
360
0
16.
Solve the equation: 2
cos
2
θ
= 1 For
0
0
=
θ
=
360
0
17.
Solve the equation: Sin
(
3
x
+
30
)
0
=
√
3
2
,for For
0
0
=
x
=
90
0
18.
Solve:4 – 4
cos
2
α
= 4sin
α
-1 For
0
0
=
α
=
360
0
19.
Solve the equation: Sin
(
2
t
+
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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