Question

what are waves?

Answer 1

So question. The functions Cosine, Sine, and Tangent are based on what concept?

Answer 2

@eljaja

Answer 3

The site was lagging and didn't show that anyone responded, I was going to repost it. Anyways.... they are based on Right-Angled Triangles I believe.

Answer 4

Very good. So let's create a right triangle. Hang on, let me switch to my tablet real quick.

Answer 5

Ok

Answer 6

So as you know, a typical right triangle would be labeled as above with sides a, b, and c. And with Angles A, B, and C. Side a is opposite Angle A. Side b is opposite Angle B and Side c is opposite angle C.

Answer 7

So what Sine, Cosine, and Tangent Functions enable us to do is find missing values such as the length of a side or the measure of an angle using information we are already given about the right triangle.

Answer 8

And so there are formulas that mathematicians came up with to help us find those unknown values.

Answer 9

For example. Suppose we need to find the value of angle A. Then we can use any of the following formulas to help us find its value:

\(\sin(A) = \dfrac{a}{c}\)

\(\cos(A) = \dfrac{b}{c}\)

\(\tan(A) = \dfrac{a}{b}\)

Which formula we use depends on the side lengths we are given.

Answer 10

I see, so in your case, basically, they give us this:
\(\cos(x) = \dfrac{b}{c} = \dfrac{1}{2}\)

In other words, \(b = 1\) and \(c = 2\). So we will input those values unto the right triangle:

Answer 11

So now, this means you know two sides of a right triangle. Any idea how we might find the third side? Hint: Does not involve any trig.

Answer 12

would it be 3?

Answer 13

What I mean is, Is there a mathematical formula for right triangles that you can think of that will enable us to find the value of the missing side, a?

Answer 14

I believe there is but I can't think of what it is.

Answer 15

Ever heard of Pythagorean Theorem?

Answer 16

I was just about to type that yeah... I was looking it up.

Answer 17

Yes, According to Pythagorean Theorem, if you have a right triangle, with sides a and b as the legs, and c as the longest side, then you can use the formula \(a^2 + b^2 = c^2\) to help find the value of the missing side.

Answer 18

Well, actually ... Here's what you should do first.

Answer 19

Start with \(a^2 + b^2 = c^2\). Then isolate the variable you need to find which is \(a\):

To do that, first subtract \(b^2\) from both sides:
\(a^2 = c^2 - b^2\)

Then square root both sides to get:
\(a = \sqrt{c^2 - b^2}\)

After that, then you can input the values b and c to the formula and solve for \(a\)

Answer 20

Looks right

Answer 21

thank you so much for your help! I appreciate it!

Answer 22

You're welcome.