Physics, asked by hamsika57, 8 months ago

find the value of theeta when 2cos theeta = 3sin theeta​

Answers

Answered by ahervandan39
0

Explanation:

Substitute

1

sin

2

(

θ

)

for

cos

2

(

θ

)

:

2

(

1

sin

2

(

θ

)

)

+

3

sin

(

θ

)

=

0

Use the distributive property:

2

2

sin

2

(

θ

)

)

+

3

sin

(

θ

)

=

0

Multiply both side by -1:

2

sin

2

(

θ

)

)

3

sin

(

θ

)

2

=

0

This is a quadratic where the variable is

sin

(

θ

)

.

It looks like it will factor:

#(sin(theta) - 2)(2sin(theta) + 1) = 0

sin

(

θ

)

=

2

and

sin

(

θ

)

=

1

2

We must discard the first root, because it is outside the range of the sine function.

Turning our attention to the second root:

sin

(

θ

)

=

1

2

Rotating counterclockwise from 0, the first encounter of this is at:

θ

=

7

π

6

The next encounter with this is at:

θ

=

11

π

6

Add integer rotations of

2

π

to both:

θ

=

7

π

6

+

2

n

π

and

θ

=

11

π

6

+

2

n

π

Where n can be any integer (positive, negative, or zero)

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