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.

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

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

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

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

d) $\displaystyle \sin(-A)=-\sin(A)$.

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.

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.

**Look at reply #3.**

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

You must reply with answers in order to get more help.

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.

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 $\displaystyle x=?~,~y=?~\&~r=~?$.

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.

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

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!**

$\displaystyle x=-4~,~y=3~\&~r=~5$. **Why?** is that so? Look at Reply #3 again.

Answer the questions.

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

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.**