Answer:
Sec(θ) = 3
Step-by-step 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.
