What is the sign of the following?

Question

sec(-θ), given that θ is in the interval (180º, 270º).

Answer 1

What is the sign of: sec(-θ), given that θ is in the interval (180º, 270º) <== 3rd Quadrant

Remember: ASTC – All Students Take Calculus (Means: Engineering Students)

* A (All) – In 1st Quadrant: All sin, cos, tan and their reciprocal csc, sec, cot Positive

* S (sin) – In 2nd Quadrant: Only sin and its reciprocal csc Positive (The rest Negative)

* T (tan) – In 3rd Quadrant: Only tan and its reciprocal cot Positive (The rest Negative)

* C (tan) – In 4th Quadrant: Only cos and its reciprocal sec Positive (The rest Negative)

Note: sec(-θ) = sec θ    and    cos(-θ) = cos θ

Therefore, all sec(-θ) = sec θ and cos(-θ) = cos θ in 3rd Quadrant are Negative

The sign of: sec(-θ) in 3rd Quadrant (in the interval (180º, 270º)) is Negative

Answer 2

sec has the same sign as cos

sec(-x)=sec(x)

In quadrant 3 sec is negative (remember AllSinTanCos)