# Thread: Exact value for trig ratios

1. ## Exact value for trig ratios

I have a question I'm having a bit of trouble with lads,

Determine the exact values for the 6 trig ratios Θ(theta) lies in the standard position with its terminal arm passing through the point P(-3,-5).

I know I'm supposed to find Sin, Cos, Tan, Csc, Sec, and Cot, but how do I find the radian measure so I can do so?

If anyone can help it would really be great, thanks so much!

2. Originally Posted by Random-Hero-
I have a question I'm having a bit of trouble with lads,

Determine the exact values for the 6 trig ratios Θ(theta) lies in the standard position with its terminal arm passing through the point P(-3,-5).

I know I'm supposed to find Sin, Cos, Tan, Csc, Sec, and Cot, but how do I find the radian measure so I can do so?

If anyone can help it would really be great, thanks so much!
to begin, did you actually draw the diagram as described?

3. Of course,

I'm assuming I have to find the angle in blue in radians, correct? Now how do I go about finding that value?

4. Originally Posted by Random-Hero-
Of course,

I'm assuming I have to find the angle in blue in radians, correct? Now how do I go about finding that value?
well, this diagram isn't complete. you need to draw a vertical line from the point where the red line touches the circle up to the x-axis. do you see the right triangle? now, do you remember SOHCAHTOA? (sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent)

do you also recall that sec(x) = 1/cos(x), csc(x) = 1/sin(x) and cot(x) = 1/tan(x) ?

do you also recall (haha, getting sick of that phrase, i bet) that in the third quadrant, only tangent and cotangent are positive, while all the other trig ratios are negative?

5. I managed to find that angle (at least I think I found it properly). First I foun the hyp. So I did (-5)^2 + (-3)^2 rooted gave me root34, then I did Sin=Opp/Hyp which was sin=(-5)/root34 which ultimately gave me -59 degrees. So I then converted that to radians, and couldn't really reduce, so know I'm stuck with 59pi/180 (or is it -59pi/180?)

So now do I find the remaining angle on the other side of the red line? and use that to find my 6 values?

6. Originally Posted by Random-Hero-

I managed to find that angle (at least I think I found it properly). First I foun the hyp. So I did (-5)^2 + (-3)^2 rooted gave me root34, then I did Sin=Opp/Hyp which was sin=(-5)/root34 which ultimately gave me -59 degrees. So I then converted that to radians, and couldn't really reduce, so know I'm stuck with 59pi/180 (or is it -59pi/180?)

So now do I find the remaining angle on the other side of the red line? and use that to find my 6 values?
if you listened to what i said, you would realize that finding the angle is completely unnecessary. you found that the hypotenuse is $\sqrt{34}$, this is correct.

now, $\sin \theta = - \frac {5}{\sqrt{34}}$

$\cos \theta = - \frac {3}{\sqrt{34}}$

$\tan \theta = \frac 53$

just by following the formulas i gave you and the directions on what to make negative and positive. see my first post. as you see, you don't need to know what $\theta$ is. now finish up