Question

someone help please ill medal

Answer 1

Important: we must know the definitions of the sine and cosine functions by heart.

If y is the angle in question, then sin y = (opposite side) / (hypotenuse), and
cos y = (adjacent side) / (hypotenuse).

Looking at your diagram, what is the length of the "opposite side?"
...of the "hypotenuse?"

Answer 2

Song, the hyp. is the longest side, so it's not sqrt(119). Try again. The length of the hyp is .... what? Length of the opp. side is ... what?

Answer 3

If I am sitting across the table from you, I'm also sitting "opposite" you.

The opp side is not 12. What is it?

Answer 4

Right. And the opp. side length is ... what?

Answer 5

But sqrt(119) is the ADJACENT side; it is next to the angle, y.
What is the "opposite side?"

Answer 6

Yes, the opp side is s. It is critically important that you know the meanings of "opp side," "adj. side" and "hyp."

sin y = opp / hyp. steal the numeric values and express sin y as the ratio of numbers.

sin y = ( ? ) / ( ? )

Answer 7

sin y = opp / hyp. What you have typed is hyp / opp (wrong order). Try again.

Note that opp = s and that hyp=12

Answer 8

Yes. Your sin y is now correct. Congrats.

Write an expression for your cosine y.

cos y = ?

Answer 9

first, as a review, type out the definition of the cosine function. Use words. cos y = ?

Answer 10

Very good. You've got it. Please, write down and review the definitions of:

cosine of x

sine of x

tangent of x

You'll have to know them by heart.

Any further questions about this problem?

Answer 11

Example: tangent x = tan x = opp / adj by definition.

Answer 12

Depends upon the context. You might be given the angle and asked to find the sine of that angle. Or you might be given the opp and hyp and be asked to find the cosine.
And so on.

But you must know those 3 definitions.

Answer 13

Remember that the sine, cosine and tangent functions have arguments, and so must be written with arguments:

sin x
cos x
tan x

not sin, cos, tan.

Answer 14

I'm confused. Is this Algebra 1??

Answer 15

Could you, Song, please write out some questions? What do you want to know?
I can tell you from long experience that you must learn the basic trig functions, sine x, cosine x and tangent x, including their definitions and when to use them.

Where do you find them? This post is an example of that. You were given an illustration of a right triangle, with the side lengths marked, and were asked to find the sine and cosine of angle y.

I could give you examples of applications of these three basic trig functions, but urge you to look for some and to share them with me first.

Answer 16

the only difference I see here is that you have found that s=5. Is that correct?

Review: Please type out the definitions of the sine, cosine and tangent functions.

Answer 17

therefore, sin y = ??

Answer 18

No problem.

First, how is the sine of x defined? (No numbers, please, just the definition).

Answer 19

Recall that we went thru the def'ns of the sine, cosine and tangent functions several times, earlier.

Answer 20

If you please, "How is the sine function defined?"

Answer 21

Then, more specifically, "how is the sine of x defined?"

Answer 22

All right. Looking at your diagram, locate angle X. What side is opp angle X? What is the hypotenuse of this triangle? Please remember, sine=5/12 is not properly written; you MUST specify an angle as the argument (input) to the sine function. In this case your argument is the angle X.

Answer 23

Type out the value of sin X.

Answer 24

Where is angle X in your diagram? Note that we are no longer talking about angle Y.
Which side is OPPOSITE angle X?

Answer 25

Write that as "the side opposite angle Y has the length sqrt(117). not "sq rt = 119"

Answer 26

The side opp angle y has the length " sqrt (117) ".

Answer 27

that's between 10 and 11.

Answer 28

OK. if the side opp to angle Y is sqrt(117), write sin X.

Answer 29

sin X = opp / hyp = ??

Answer 30

@song_of_the_sole: still interested in finishing this problem?

Answer 31

I meant sqrt(119). Apologies.

sin X = ?

cos X = ?

Answer 32

Great. Could you stretch this out and find tan X?

Answer 33

Does that represent tan x = opp / adj?

Answer 34

What is the length of the adj side? (adj to angle X)

Answer 35

Very good. Any questions?

Answer 36

Can't answer that without knowing specifically what you mean by "the ratios fro sin X and cos X."

Do you, perhaps, mean "the ratio of sin X TO cos X?"

or do you mean "cos X = sqrt(119)/5," which, after all, is a ratio?

Answer 37

Note that sin X = sqrt(119) / 12 is also a ratio.

Answer 38

OK, if you're supposed to write "ratios" for the individual sine and cosine functions, separately, then sin X = sqrt(119) / 12 and cos X = 5/12.

Answer 39

These are my interpretations of your homework questions.

Answer 40

Definitely leave them as is; there is nothing to "solve for." Actually, you are "evaluating" the sine and cosine functions for this triangle and its angle X.