if sec theta = 2 , theta belongs to ]270 , 360[ , then theta =

Answer 1

Using the given information, we can say that sec(θ) = 2.

Recall that sec(θ) is the reciprocal of cosine(θ). So we have:

sec(θ) = 2
1/cos(θ) = 2

Multiplying both sides of the equation by cos(θ), we get:

1 = 2cos(θ)

Dividing both sides by 2, we have:

1/2 = cos(θ)

Since θ belongs to ]270, 360[, we know that θ is an angle in the fourth quadrant. In the fourth quadrant, cosine values are negative.

So, cos(θ) = -1/2.

Therefore, θ = arccos(-1/2) = 150 degrees.

Hence, the value of theta in radians would be θ = (150 * π)/180 = (5π)/6 radians.