Question

Explain the difference between using the cosine ratio to solve for a missing angle in a right triangle versus using the secant ratio. You must use complete sentences and any evidence needed (such as an example) to prove your point of view.

Answer 1

@Tranquility

Answer 2

@Tranquility @Ultrilliam

Answer 3

@Tranquility

Answer 4

Keep in mind that the cosine ratio and the secant ratio can only be used if we have a right triangle.

Also, you must know that
\( \Large\sec \theta = \frac{1}{\cos \theta}\)

In the triangle I drew,
\(\Large \cos \theta = \frac{y}{\sqrt{x^2+y^2}}\)
And
\(\Large \sec \theta = \frac{\sqrt{x^2+y^2}}{y}\)

We can use either ratio to solve for a missing angle.

Answer 5

erm...

Answer 6

so should i just create a right triangle and put in random values and solve for a missing angle?

Answer 7

@AMQ There are no errors in whatever you wrote. I believe an example with numbers might be more easier to make a case.



\(\Large \cos\theta = \frac{\sqrt{3}}{2}\)
\(\Large \theta = \arccos(\frac{\sqrt{3}}{2}) = 30^o\)

And you will notice that if you used the secant ratio, you would get the same answer
\(\Large \sec\theta = \frac{2}{\sqrt{3}}\)
\(\Large \theta = \text{arcsec}(\frac{2}{\sqrt{3}}) = 30^o\)

Answer 8

Thanks a lot. :)

Answer 9

My pleasure!

Answer 10

@Tranquility why is it arccos and arcsec? :/

Answer 11

cos of an angle gives you a value

For example
cos(60) = 1/2

What if instead you're given 1/2 and told to find the angle?
That's where arccos comes in and let's us do the reverse operation so that if we know the value, we can find the angle.

arccos(1/2) = 60

Also there are multiple angles that can be found from a given value. Have you learned about the unit circle yet?

Answer 12

nope :/

Answer 13

correct me if i'm wrong, but since the square root of 3 divided by 2 = 0.866025405, we would have to find arccos of that to get the angle? @Tranquility

Answer 14

Yes, and you would need to use a calculator to do that. Unless we're given a value for which we know the angle such as 1/2 or sqrt(3)/2

Answer 15

Okay, I got it. Thanks again. :)

Answer 16

No problem!