# Find trig functions on unit circle.

• April 28th 2013, 02:54 PM
FatimaA
Find trig functions on unit circle.
I'm having trouble with this problem. My professor never showed how to get the answers in the key, so I have no idea how to solve these.

6) Suppose that sinA = 3/5 and tanA<0. Find the following. Clearly explain your reasoning and draw pictures (when appropriate) to help justify your answer.

a) cosA

b) tanA

c) sin(A+pi)

d) sin(-A)

Thanks beforehand for the help.
• April 28th 2013, 03:08 PM
topsquark
Re: Find trig functions on unit circle.
Quote:

Originally Posted by FatimaA
I'm having trouble with this problem. My professor never showed how to get the answers in the key, so I have no idea how to solve these.

6) Suppose that sinA = 3/5 and tanA<0. Find the following. Clearly explain your reasoning and draw pictures (when appropriate) to help justify your answer.

a) cosA

b) tanA

c) sin(A+pi)

d) sin(-A)

Thanks beforehand for the help.

What have you been able to do with these?

-Dan
• April 28th 2013, 03:15 PM
Plato
Re: Find trig functions on unit circle.
Quote:

Originally Posted by FatimaA
6) Suppose that sinA = 3/5 and tanA<0. Find the following. Clearly explain your reasoning and draw pictures (when appropriate) to help justify your answer.
a) cosA
b) tanA
c) sin(A+pi)
d) sin(-A)

Recall that if $\sin(A)>0~\&~\tan(A)<0$ then $A\in II$.

Now $\sin(A)=\frac{y}{r},~\cos(A)=\frac{x}{r},~\&~r^2=x ^2+y^2~.$

c) $\sin(A+\pi)=-\sin(A)$.

d) $\sin(-A)=-\sin(A)$.
• April 28th 2013, 03:23 PM
FatimaA
Re: Find trig functions on unit circle.
I haven't been able to get anywhere, really. Looking back through my notes, I get lost. I don't know which identities I'm supposed to use.
• April 28th 2013, 03:29 PM
Plato
Re: Find trig functions on unit circle.
Quote:

Originally Posted by FatimaA
I haven't been able to get anywhere, really. Looking back through my notes, I get lost. I don't know which identities I'm supposed to use.

What are $x=?~,~y=?~\&~r=~?$.

• April 28th 2013, 03:39 PM
FatimaA
Re: Find trig functions on unit circle.
Ok I worked with reply 3. I am supposed to use the even-odd properties? I don't know how you got -sinA from sin(A+pi).

For d and c, I got -3/5.

I'm lost on a and b. I don't know how to use the information. My teacher got -4/5 for a but when I attempted it I had -3/5.
• April 28th 2013, 03:58 PM
Plato
Re: Find trig functions on unit circle.
Quote:

Originally Posted by FatimaA
Ok I worked with reply 3. I am supposed to use the even-odd properties? I don't know how you got -sinA from sin(A+pi).

For d and c, I got -3/5.

Look, you did not do as I asked you to do.

What are $x=?~,~y=?~\&~r=~?$.

Until you can answer that, there no hope for you to understand this question.

If you don't want to learn how to do do this, then don't answer.
• April 28th 2013, 04:18 PM
FatimaA
Re: Find trig functions on unit circle.

y^2 = (sinA)^2, x^2 = (cosA)^2, r^2 = 1

x^2+y^2=1

(3/5)^2+x^2=1

9/25+x^2=1

x^2 = -16/25

x = -4/5
• April 28th 2013, 04:29 PM
Plato
Re: Find trig functions on unit circle.
Quote:

Originally Posted by FatimaA

y^2 = (sinA)^2, x^2 = (cosA)^2, r^2 = 1

x^2+y^2=1

(3/5)^2+x^2=1

9/25+x^2=1

x^2 = -16/25

x = -4/5

NO!
$x=-4~,~y=3~\&~r=~5$. Why? is that so? Look at Reply #3 again.

• April 28th 2013, 04:46 PM
FatimaA
Re: Find trig functions on unit circle.
sinA = 3/5

sinA = y/r

cosA = x/r

y^2 + x^2 = r^2

y = 3, r = 5

3^2 + x^2 = 5^2

9+ x^2 = 25

x^2 = 16

x = 4 but because it's in quadrant II it is -4

so cosA = -4/5
• April 28th 2013, 04:51 PM
Plato
Re: Find trig functions on unit circle.
Quote:

Originally Posted by FatimaA
sinA = 3/5
sinA = y/r
cosA = x/r
y^2 + x^2 = r^2
y = 3, r = 5
3^2 + x^2 = 5^2
9+ x^2 = 25
x^2 = 16
x = 4 but because it's in quadrant II it is -4
so cosA = -4/5

Yes, now you have it.