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

Help Me Please Im Really Behind

Answer 2

@ganeshie8 @amistre64 @mathmale

Answer 3

I only have this and another question left

Answer 4

woow, i dont know this yet sorry :)

Answer 5

Im in 10th grade

Answer 6

First, some basics:

Knowing the definitions of the sine and cosine function is essential. What are these definitions?

For example: \[\tan x = \frac{ opposite~side }{ adjacent~side }\]

Answer 7

Write out similar definitions for the sine and cosine of the angle x.

Answer 8

Sine is opposite/ hypotenuse and cosine adjacent/ hypotenuse and if they equal 90 they must be complemantary angles

Answer 9

Next: Note that x and y are "complementary angles." What does that mean to you?

Answer 10

That they equal to 90 degrees

Answer 11

Nice work; just a little tweak to the wording: If the SUM of x and y is 90 degrees, then x and y are complementary angles. (You must mention the word "sum.")

Answer 12

Ok

Answer 13

Now look at angle x. Which side of this triangle is "opposite" angle x?
Which side is the hypotenuse?

Knowing these two values, find the ratio
opp side
sin x = --------------
hyp

Answer 14

which must be a fraction between 0 and 1.

Answer 15

Sin x = 3/4

Answer 16

is that it?

Answer 17

No, unfortunately. Your 3/4 is the TANGENT of the angle x.

You correctly defined the SINE of angle x. Find sin x using the appropriate side lengths given in the figure.

Answer 18

If the 2 "legs" of this triangle are 3 and 4 respectively, what is the length of the hypotenuse? Hint: use the Pythagorean Theorem to find the length of the hyp.

Answer 19

Umm lets see

Answer 20

Those trig functions and the Pyth Theorem are extremely important and are worth memorizing and practicing.

Answer 21

a*2 + B*2 = C*2
3*2 + 4*2 = C*2
9 + 16 = C*2
25 = c*2
c = 5

Answer 22

is this correct

Answer 23

yes, the length of the hyp is 5. So the sine of x is what fraction?

Answer 24

Sin x = 3/5

Answer 25

Great. Got it.

For review: What is the definition of the cosine function?

Answer 26

What is cos x?

What is cos y?

Answer 27

cosine is adjacent/hypotenuse

Answer 28

4/5

Answer 29

cos x = 4/5

Answer 30

Great. That's the definition. Now, what is cos x?

Right you are.

Now, what is cos y?

Answer 31

cos y ? umm im a little confused what is cos y?

Answer 32

The principle is exactly the same. Find angle y. Identify its adjacent side and its hypotenuse. Write the cosine of y exactly as you did before:

cos y = adj / hyp

Answer 33

So it would be cos x = 4/5

Answer 34

So this would mean that my answer is sin x = 3/5 and cos y = 4/5 correct

Answer 35

And that there relationship would be that there sum is to 92 degrees meaning that there complemantary correct?

Answer 36

90 degrees my bad

Answer 37

@mathmale

Answer 38

@amistre64 can you help me finish up

Answer 39

@ganeshie8

Answer 40

Anyone

Answer 41

@phi

Answer 42

@phi mathmale is offline I just need to know if its correct

Answer 43

where are you in the question ?

Answer 44

. Find the value of sin x° and cos y°

you should get the same ratio for these.

Answer 45

Sorry umm we are done with the question I just need to know if its correct

Answer 46

to do this use the definitions (people use SOH CAH TOA to remember them)
sin use SOH: sin= opp/hyp

sin x means put your finger on the x angle. go "across" to the other (i.e. opposite ) side and read off 3
as you know , they hypotenuse is 5, you get sin x = 3/5
I

Answer 47

Yes and cos is cos x = 4/5

Answer 48

There complemantary which means that they sum up to 90 degrees thats there relationship that they share together.

Answer 49

now do cos y°

cos: CAH cos= adjacent/hyp

put you finger on angle y. Find the adjacent side . It is the side that makes up part of the angle but is NOT the hypotenuse. You should find 3
cos y = 3/5

Answer 50

I got it now. Can you help me with one last question please.

Answer 51

An observer (O) is located 660 feet from a tree (T). The observer notices a hawk (H) flying at a 35° angle of elevation from his line of sight. How high is the hawk flying over the tree? You must show all work and calculations to receive full credit.

Answer 52

you found cos x , but they want cos y

Answer 53

if you are doing a different question, pleasemake a new post.

Answer 54

arent cos x and y the same thing