Question

I need help with Sin, Cos, Tan with respect to a function of a angle.
So I have:
x-coordinate as -2sqrt3 adjacent angle
y-corrdinate as -4 (opposite angle
r-radius is what i can't figure out how to get.
I know in general its r=sqrt((-4)^2+(-2sqrt3)^2)
can someone tell me what the radius/hypotenuse is?

Answer 1

actually dont tell me, show me how to figure it out..
\[r=\sqrt{(-4)^{2}+(-2\sqrt{3)}^{2}}\]

Answer 2

Radius would be the hypotenuse, which is c is a\[a ^{2} + b ^{2} = c ^{2}\]

So to find the radius you would solve for C, or in this case, R.

R = \[\sqrt{a ^{2} + b ^{2}}\]

Answer 3

right i do see that, when im getting sucked on ir the -2sqrt3 under the radical
that I'm unsure how to handle

Answer 4

So you would now get \[\sqrt{16 + 12}\]

Then \[\sqrt{28}\] which is equal to \[2\]

Answer 5

*\[2 \sqrt{7}\]

Answer 6

hum, how did you get 12?

Answer 7

Basically what i do is square 2 (or the number outside the radical) and multiply it to the inside number to get 4 x 3, thus ending up with \[\sqrt{12}\]

Answer 8

and when you square a root, you get the number inside

Answer 9

oh i see, and that applys to all radicals in that form
?

Answer 10

Yes, another thing you could do is square the 2 √3 separately , getting 4 and 3, and since 2√3 is 2 X √3 , you would still multiply 4 x 3, getting 12. Whichever way you find easier.

Answer 11

ok and lastly the book says
SIN is - (2sqrt7/7)
how

Answer 12

is this the same problem?

Answer 13

yes

Answer 14

im getting kicked out our UC when i get back to my dorm i will check this in 10 mins

Answer 15

Ok, but basically since sin is opp/hyp, which is y/r and we established that the hyp is 2√7 , we would get y/2√7 . The Opposite is -4. This leaves you with -4/(2√7). This simplifies to -2/√7. But we arent done yet. You can't leave a radical in the bottom of a fraction. Basically you have to multiply the top and bottom by the square root to cancel it out,

\[\frac{2 }{ \sqrt{7}} \times \frac{ \sqrt{7} }{ \sqrt{7} }\]

Resulting in \[\frac{ 2\sqrt{7} }{ 7 }\]

Answer 16

oh yes, i totally got it, when you put it like that, i forgot that simple rule

Answer 17

thank you so much for your hlep with ithis, it was driving me nuts!

Answer 18

haha no problem

Answer 19

;)