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Determine all solutions to the equation 1 over cosine theta equals 4 times cosine theta on the interval [0, 2π).

open bracket pi over 3 comma 2 times pi over 3 comma 4 times pi over 3 comma 5 times pi over 3 close bracket
open bracket pi over 3 comma 5 times pi over 3 close bracket
open bracket pi over 6 comma 5 times pi over 6 comma 7 times pi over 6 comma 11 times pi over 6 close bracket
open bracket pi over 6 comma 11 times pi over 6 close bracket

Sagot :

mahinkhan48099

Answer:I think over 3.

Step-by-step explanation:

open bracket pi over 3 comma 2 times pi over 3 comma 4 times pi over 3 comma 5 times pi over 3 close bracket

open bracket pi over 3 comma 5 times pi over 3 close bracket.

The solution of the trigonometric function will be π/3, 2π/3, 4π/3, and 5π/3. Then the correct option is C.

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The trigonometric equation is given below.

1/cos θ = 4 cos θ

The interval of the cos θ is [0, 2π).

Simplify the trigonometric equation, then the equation will be

cos² θ = 1/4

Taking square root on both side, then the equation will be

cos θ = ±1/2

Taking cosine inverse, then the equation will be

θ = cos ⁻¹(1/2)

θ = π/3, 2π/3, 4π/3, 5π/3

The solution of the trigonometric function will be π/3, 2π/3, 4π/3, and 5π/3.

Then the correct option is C.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

#SPJ5

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