Question

Find the general value of theta , when sec theta,= 2/root 3 answer with explanation ​

Answer 1

Answer: θ = ( 2nπ - π/6 )

Explanation:

sec θ = 2 /√ 3.

or, cos θ = cos π /6.

or, θ = 2 n π - π/6 where n is an integer.

θ is always positive when it is located on 4 th co- ordinate.

Answer 2

Answer:

The general value of theta is  2nπ ± π/6.

Explanation:

We are given that secθ = $\frac{2}{\sqrt{3} }$

No, values of secθ repeat after an interval of 2π. Therefore,

θ = 2nπ + π/6 and θ = 2nπ + 2π - π/6

θ = $2n\pi +\frac{\pi }{6}$ and θ = $2(n+1)\pi -\frac{\pi }{6}$, where n ∈ Z.

Combining the above two values, we get

θ =  2nπ ± π/6, where n ∈ Z.

Therefore, the general solution of secθ = $\frac{2}{\sqrt{3} }$ is 2nπ ± π/6.

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