The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric values of the angle. (2/3, 5/8)

Question

anonymous · Answer

I know how to get the sin, cos, tan and their reciprocals, but I'm having trouble with the fractions. I know that you need to apply $$r=\sqrt{x^2+y^2}$$ first, but getting the answer is stumping me.

aum · Answer

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aum · Answer

$$r^2 = \left (\frac 23\right )^2 + \left(\frac 58 \right)^2 = \frac {4}{9} + \frac{25}{64}   $$

anonymous · Answer

And this is where I am stuck

aum · Answer

$$r^2 =  \frac {4}{9} + \frac{25}{64}  = \frac{4*64+25*9}{9*64} = \frac{256+225}{9*64} = \frac{481}{9*64} \ r = \frac{\sqrt{481}}{3*8}= \frac{\sqrt{481}}{24}$$

anonymous · Answer

ah, fractions. always hated these. can you explain to me what exactly happened there?

aum · Answer

$$\frac ab + \frac cd = \frac{ad + bc}{bd}$$

anonymous · Answer

and here I am, back to algebra 1. totally forgot about the identities of fractions. 
so now we have $$\frac{ \sqrt{481} }{ 24 }$$ then what? would we just apply sin= y/r, cos=x/r and tan = y/x and their inverses?

aum · Answer

Exactly.

And if you get a radical in the denominator, get rid of it by multiplying top and bottom by the radical in the denominator.

aum · Answer

Many teachers and textbooks don't like radicals in the denominator and so you have o rationalize the denominator.

bossimbacon · Answer

@aum  can you plz help me I'm sorry @bbbbbrrrruuuuhhhh  but no one is answering my questions

anonymous · Answer

Nice, I think I got the questions right. It is a bit tedious typing them in, thank you for your help, friend.

aum · Answer

You are welcome.