Question

Sketch a triangle that has acute angle θ, and find the other five trigonometric ratios of θ.

Tan(degree sign)= sqr of 15

Answer 1

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

Answer 2

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

Answer 3

Does that seem right so far?

Answer 4

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 :)

Answer 5

I can keep going XD

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

I can't seem to figure that one out.

Answer 11

Is everything else right?

Answer 12

Yes

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

Oh okay, welcome! XD

Answer 17

you got it?

Answer 18

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.

Answer 19

ok...gonna need the picture tho :)

Answer 20

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

Answer 21

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

Answer 22

Yes, that pic.

Answer 23

LIKE THIS? opps caps were on lol

Answer 24

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

Answer 25

are we dealing with a right triangle?

Answer 26

yes

Answer 27

A is bottom left angle?

Answer 28

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

Answer 29

Here!

Answer 30

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

Answer 31

Sorry :[

Answer 32

'sok....ill live ;)

Answer 33

x is equal to "sin(t)"

sin(t) = x/y

x = y * sin(t)

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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 :)

Answer 38

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....

Answer 39

you know how the trig functions are defined?

Answer 40

Not really.

Answer 41

What do I do for this problem though?
\

Answer 42

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.

Answer 43

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

Answer 44

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

Answer 45

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

Answer 46

How would I find x and y then?

Answer 47

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.

Answer 48

That's all it shows in the problem.

Answer 49

no angle or anything.

Answer 50

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

Answer 51

Here is another similar one if you can help with this one.

Find the side labeled x. Assume a = 4.

Answer 52

How would I express them in terms then?

Answer 53

this we have enough information to solve :)

Answer 54

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

Answer 55

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

Answer 56

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

Answer 57

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

Answer 58

Same for y!

Answer 59

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

Answer 60

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)

Answer 61

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

Answer 62

do you have anymore options :)

Answer 63

nope :(

Answer 64

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

Answer 65

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

Answer 66

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

Answer 67

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

Answer 68

Are you in college or what?