Question

2sin^ 2theta+3sintheta=0 find the permissible values of cos theta

Answer 1

Permissible value of cosθ = 1

Step-by-step explanation:

Given,

2 sin²θ + 3 sinθ = 0

or, sinθ (2 sinθ + 3) = 0

∴ either sinθ = 0 or, 2 sinθ + 3 = 0

Then sinθ = 0 or, sinθ = - 3/2

∵ - 1 < sinθ < 1, the only value of sinθ = 0

Now, sinθ = 0 gives θ = 0

and cosθ = cos0 = 1

∴ the permissible value of cosθ = 1

[[ To find the general solution, we write

cosθ = 1

or, θ = 2nπ, where n is an integer.

Therefore the general solution is 2nπ. ]]

Trigonometry:

Trigonometry is the study of relations between angles and their ratios with various properties to find sine, cosine, tan, cosec, sec and cot ratios. Some properties can deduce angles in their general value apart from known definite ones. Now let us know some identities-

1. sin²θ + cos²θ = 1

2. sec²θ - tan²θ = 1

3. cosec²θ - cot²θ = 1

Answer 2

cos² ø = ± 1

Step-by-step explanation:

2 sin ø + 3 sin ø = 0

sin ø ( 2 sin ø + 3 ) = 0

sin ø = 0 , 2 sin ø = - 3

sin ø = 0 , sin ø = -3 / 2

since, -1 < sin ø < 1

sin ø = 0

√sin²ø = 0

√ 1 - cos² ø = 0

squaring both sides

1 - cos² ø = 0

1 - cos² ø = - 1

cos² ø = 1