Sketch a triangle that has acute angle θ, and find the other five trigonometric ratios of θ.
Tan(degree sign)= sqr of 15

- anonymous

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- anonymous

sin(θ) =
cos(θ) =
csc(θ) =
sec(θ) =
cot(θ) =

- anonymous

I'll take a shot at it.....
So tan is sin/cos which is y/x
So x = 1 and y = sqrt15
Then do x^2 + y^2 = r^2

- anonymous

Does that seem right so far?

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- anonymous

I have no idea. I'm been trying to figure this out for a while now. Thanks for trying! If it is right kudos to you :)

- anonymous

I can keep going XD

- anonymous

So x^2 + y^2 = r^2 (r is the hypotenuse)
(1)^2 + (sqrt15)^2 = r^2
1+ 15=r^2
16=r^2
sqrt16=r
r=4

- anonymous

So now you have all the needed numbers to finish the problem.
x = 1
y = sqrt15
r = 4

- anonymous

sin = sqrt15/4
cos = 1/4
tan = sqrt15
csc = 4/sqrt15
sec = 4
cot = 1/sqrt15

- anonymous

Thank you so much! But the Sin= sqrt15/4 is not the right answer.

- anonymous

I can't seem to figure that one out.

- anonymous

Is everything else right?

- anonymous

Yes

- anonymous

Is it (sqrt15)/4 or is the 4 inside the sqrt of 15?

- anonymous

It is (sqrt15)/4 because it is y/r.

- anonymous

Ok, yeah that's the right answer. Thanks again :)

- anonymous

Oh okay, welcome! XD

- amistre64

you got it?

- anonymous

Yeah. But I have another problem.
Use the figure and the value given below to answer the following questions. Assume A = 4.
(a) Express x in terms of trigonometric ratios of θ.
(b) Express y in terms of trigonometric ratios of θ.

- amistre64

ok...gonna need the picture tho :)

- amistre64

or use this to let me know what I am looking at :)

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- anonymous

A is the Adjacent angle, y is the hypotenuse, and x is the opposite. Acute triangle.

- anonymous

Yes, that pic.

- amistre64

LIKE THIS? opps caps were on lol

- amistre64

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- anonymous

The A is on the bottom, but everything else is in the right place.

- amistre64

are we dealing with a right triangle?

- anonymous

yes

- amistre64

A is bottom left angle?

- anonymous

Just the bottom angle. I'll try to put up the pic

- anonymous

Here!

##### 1 Attachment

- amistre64

ahhh...thats better, when you said A was the adjacent angle it threw me :)

- anonymous

Sorry :[

- amistre64

'sok....ill live ;)

- amistre64

x is equal to "sin(t)"
sin(t) = x/y
x = y * sin(t)

- amistre64

probably want my to use A for that eh....

- amistre64

A = 4...that helps....

- anonymous

I don't understand how to use it in the equation.

- amistre64

I think its asking for all the trig functions that use the "x" there and how we would solve for "x":
x = yadayadayada stuff like that, might be overkill, but better safe than sorry :)

- amistre64

sin(t) = x/y ; x = y * sin(t)
csc(t) = y/x ; x = y/csc(t)
tan(t) = x/4 ; x = 4tan(t)
cot(t) = 4/x ; x = 4/cot(t)
thats all of them thatll use the x....

- amistre64

you know how the trig functions are defined?

- anonymous

Not really.

- anonymous

What do I do for this problem though?
\

- amistre64

the names that are given to them arent all that important, but since they got em, might as well use em.
sin is simply the ration of the opposite side from the angle divided by the hypotenuse: usually abbreviated as opp/hyp.

- amistre64

you just express x or y in terms of the trig functions... as far as I can tell

- amistre64

...simply the *ratio* of the .....

- amistre64

oonce you know sin and cos, the rest are just made with these two...

- anonymous

How would I find x and y then?

- amistre64

you would need more information to actually solve for x and y; you would need to know the measurement of an angle, or another side so that you could work things out. But what you have is not enough information to get any "solid" answers for the rest of it.

- anonymous

That's all it shows in the problem.

- anonymous

no angle or anything.

- amistre64

then it cant expect you to "solve" for any values, just want you to be able to express what x and y are in terms of the rest of the information

- anonymous

Here is another similar one if you can help with this one.
Find the side labeled x. Assume a = 4.

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- anonymous

How would I express them in terms then?

- amistre64

this we have enough information to solve :)

- amistre64

well, I wrote up all the ones I could think of for the x values up there.

- amistre64

if a = 4 then sin(60) = x/4
sin(60) is one of those basic angles you learn in trig class and are expected to memorize. the sin(60) = sqrt(3)/2
sqrt(3) x
----- = ---
2 4
2sqrt(3) = x is as far as you can go without a calculator

- anonymous

Oh.. ok I get this one. But the other has me confused :P

- anonymous

It just says "Express x in terms of trigonometric ratios of θ."

- anonymous

Same for y!

- amistre64

the other one just says:
(a) Express x in terms of trigonometric ratios of θ.
(b) Express y in terms of trigonometric ratios of θ.
it doesnt say "solve" for any particular value. Just use what you know about the trig functions to be able to express x or y in terms of them

- amistre64

like this:
sin(t) = x/y ; x = y * sin(t)
csc(t) = y/x ; x = y/csc(t)
tan(t) = x/4 ; x = 4tan(t)
cot(t) = 4/x ; x = 4/cot(t)

- anonymous

How would I go about doing that? I tried the X ones you put up, but they don't seem to work.

- amistre64

do you have anymore options :)

- anonymous

nope :(

- amistre64

then I would just skip it and move to the next question..... :)

- amistre64

lifes to short to worry about 1 trig problem that they dont give you enough information about right ?

- anonymous

Haha... Thanks so much for your help. I'm actually learning math more from you than my stupid professor lol :)

- amistre64

lol .... well, I do have the time.....alot of time :)

- anonymous

Are you in college or what?

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