Solve the following equation for values of theta between 0 and 360 degrees

Question

2sec²theta-3tan theta - 1=0

Answer 1

Solve the following equation for values of theta between 0 and 360 degrees
8sin²theta + 6cos theta - 9= 0

Answer 2

θ
=
2.678
or
2.3562
radians

Explanation:
As
sec
2
θ
=
1
+
tan
2
θ

2
sec
2
θ
+
3
tan
θ
=
1
can be written as

2
+
2
tan
2
θ
+
3
tan
θ
=
1

or
2
tan
θ
+
3
tan
θ
+
1
=
0

i.e.
(
2
tan
θ
+
1
)
(
tan
θ
+
1
)
=
0

Hence either
tan
θ
=
−
1
2
=
tan
(
π
−
0.4636
)
=
tan
2.678
(in radians)

or
tan
θ
=
−
1
=
tan
(
3
π
4
)
=
tan
2.3562
(in radians)

These are results in
[
0
,
π
]

Answer 3

for the second one, Step 1. Find the value of :

Given,





Divide the above equation by 5:








Step 2. Let


and


.(Consider)








are the solutions of the given equation.

or




Step 3. Take “sin” on both sides, we get

Answer 4

2sec^2θ-3tanθ - 1 = 0
2(1+tan^2θ)-3tanθ-1 = 0
2tan^2θ - 3tanθ + 1 = 0
(2tanθ-1)(tanθ-1) = 0
tanθ = -1/2
tanθ = 1
now finish it off

same idea.
8sin^2θ + 6cosθ - 9= 0
8cos^2θ - 6cosθ + 1 = 0
(4cosθ - 1)(2cosθ - 1) = 0
cosθ = 1/4
cosθ = 1/2
and so on