Question

Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of sin x° and cos y° share?

Answer 1

for this you need to remember that sine, for a right triangle, is "opposite over hypotenuse"

Answer 2

alrighty

Answer 3

what is the length of the side opposite angle \(x\)?

Answer 4

in this case we,re trying to find the value of sin x and cos y

Answer 5

yes, lets find \(\sin(x)\) first
length of side opposite angle \(x\) is ?

Answer 6

so it would be 8 divided by an unknwon number which in this case is the hypoteneuse

Answer 7

@satellite73

Answer 8

it is not unknown

Answer 9

you find it by using pythagoras, if you have not memorized this particular right triangle yet

Answer 10

im sorry what is that? math has never been my strong suit

Answer 11

@satellite73

Answer 12

\[a^2+b^2=c^2\] for a right triangle with legs \(a,b\) and hypotenuse \(c\)

Answer 13

ah okay, let me write that down

Answer 14

@satellite73 so \[x ^{2}+y ^{2}= z ^{2}\]

Answer 15

no
in your case \[15^2+8^2=c^2\]

Answer 16

ohh i see

Answer 17

in your case \(x\) and \(y\) are supposed to represent angles, the sides are 8 and 15

Answer 18

alright now i solve for the equation correct?

Answer 19

@satellite73 so 289 squared?

Answer 20

Sorry if im far off and do i need to constantly add your name for a reply or do you still get them?

Answer 21

15 times 15 is 225, 8 times 8 is 64

Answer 22

it is \[15^2+8^2=c^2\] so \[289=c^2\] but you want \(c\) so take the square root of 289

Answer 23

ahh

Answer 24

so 17 squared???

Answer 25

no just 17

Answer 26

ok

Answer 27

So that is the new figure given after solving that equation. Now we can solve for sin x and cos y???

Answer 28

at the risk of repeating myself, since is "opposite over hypotenuse"

Answer 29

ok lol so 8 divided by 17

Answer 30

yeah, but don't divide, just write \[\sin(x)=\frac{8}{17}\]

Answer 31

alright i wrote it down

Answer 32

would it turn out to be 17 Sin(x) = 8

Answer 33

hello @mathmale

Answer 34

just incase its lagging, im going to refresh page real quick

Answer 35

Valid approach.

An alternative approach would be to recognize that x and y are "complementary" angles, meaning that their sum is 90 degrees. They have this property: sin x = cos y.

Another alternative:

Focus on the side of length 8. 8=17cos y. But also, 8=17 sin x. Thus, sin x = cos y.

Answer 36

Hello, thatawayz!

Answer 37

@mathmale but what if they are not complentary? one could be 30, the other 60

Answer 38

Glad you're interested enough to ask a question like that.

However, 30 deg. and 60 deg. ARE complementary, so sin 30 = cos 60, cos 30 = sin 60, and so on.

Answer 39

woah, im sorry i just had a major brainfart lol

Answer 40

i was under the assumption that complimentarys had to be both at an equal angle so 45 and 45

Answer 41

clearly not the case lol

Answer 42

alright, @mathmale what is our next step?

Answer 43

You have already found that the hypotenuse has length 17.

Therefore, sin x=8/17, and this is the same as cos y, because x and y are complementary angles.

Answer 44

alright so we just solve for each one right?

Answer 45

No; we're done.

How would you answer "What relationship do the ratios of sin x° and cos y° share?"

Answer 46

note that sin x is a ratio, as is cos y.

Answer 47

The relationship between the two is that they are both complimentary angles

Answer 48

both would add to 90

Answer 49

that's true. What about the ratios sin x = 8/17 and cos y=8/17?

Answer 50

Both sin x and cos y are equal to ... ??

Answer 51

that must mean they equal the same thing correct?

Answer 52

Yes, and that "same thing" is 8/17. :)

Answer 53

45

Answer 54

Nope. Sorry about that.

Answer 55

We haven't found either of the 2 unknown angles, have we?

Answer 56

If sin x = 8/17, what is x? Use the inverse sine function to answer that.
Express your answer in degrees.

Answer 57

no, i think thats what might have thrown me off a bit and was why i was asking extensively about the whole 8/17 thing

Answer 58

answer to 8/17 is 0.47

Answer 59

The 2 legs of the triangle are given, and satellite73 helped you to find the hypotenuse.
That's where we get sin x = 8/17.

You have divided 8 by 17. No.

What we want is the value (measure) of x when sin x = 8/17.

\[\sin ^{-1}\frac{ 8 }{ 17 }=?\]

Answer 60

Have you done a similar problem on your calculator? You might need to set the MODE to 'degrees.'

Answer 61

ahh, no need i have a ti84 plus

Answer 62

hold up, let me grab it real quick