Question

The line y=3x creates an acute angle theta when it crosses the x-axis, Find the exact value of sec theta

Answer 1

Sec(θ) = 3

Explanation:

First, we know that:

Sec(x) = 1/Cos(x)

Now we have an angle θ in the intersection between the line y = 3x and the x-axis.

Here we can think of this as a triangle rectangle, such that:

x is the adjacent cathetus to θ

y is the opposite cathetus to θ

y = 3*x is the hypotenuse.

Here we also need to remember the relation:

Cos(θ) = (adjacent cathetus)/(hypotenuse)

Then we will get:

Cos(θ) = x/(3*x) = 1/3

If we multiply both sides by 3, we get:

Cos(θ)*3 = (1/3)*3 = 1

Cos(θ)*3 = 1

Now we can divide both sides by Cos(θ)

[Cos(θ)*3]/Cos(θ) = 1/Cos(θ)

3 = 1/Cos(θ)

And 1/Cos(θ) = Sec(θ)

Then:

3 = Sec(θ)

The exact value of sec theta is 3.