Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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

Sagot :

facundo3141592

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.

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.