Question

a point (x,y) on a unit circle corresponds to a real number "t" for 3pi/2 < t < 2pi. find 5tant-2csct+cos^2^t when P(x,y)=(3/5, -4/5). simplify answer completely. for my equation i got 5tan(-4/3)-2(-5/4)+3cos(3/4)^2^. how do i simplify that?

Answer 1

you get beat me phi lol

Answer 2

I used a smaller picture!

Answer 3

yours looks a lot better

Answer 4

Go ahead, and finish this...

Answer 5

ok if you insist we need to find the hyp.
we know the pythagroean thm so we can do this

Answer 6

\[hyp=\sqrt{(\frac{3}{5})^2+(\frac{-4}{5})^2}=\sqrt{\frac{1}{5^2}}\sqrt{(3)^2+(-4)^2}\]

Answer 7

\[=\frac{1}{5}\sqrt{9+16}=\frac{1}{5}\sqrt{25}=\frac{5}{5}=1\]

Answer 8

also theta=t
this is the angle in this case

Answer 9

so we find tan(t)
tan(t)=opp/adj

Answer 10

tan(t)=(-4/5) / (3/5)=(-4/5) (5/3)=-4/3
now can you find csc(t) and cos(t) ?

Answer 11

ok i got that. now to simplify it in the entire equation am i using referance angles with their corresponding algebraic signs to find the correct values?

Answer 12

not sure what you are asking. Just try one, say 2 csc(t)

Answer 13

well if i substitute the value for tan in the equation i get 5tan(-4/3)-2(-5/4)+3cos(3/5)^2^. how do i simplify that?

Answer 14

Here's the main idea:
tangent is a ratio of sides of a right triangle. In our case, with angle t, we have a triangle withs sides 3/5 (for x), -4/5 for y, and 1 for the hypotenuse.

So tangent of t is the length of the opposite side (here y) over the the length of the adjacent side (here x). tan(t)= -4/5 over 3/5

Answer 15

so solving for than tan=(-4/3) right? but thats just the first step. now i have to take that value and simplify that expression

Answer 16

OK. now find csc(t)

Answer 17

csc=1/sin=1/-4/5...therefore csc=(-5/4)

Answer 18

So you have the idea now.

Answer 19

you need cos^2(t), plug all these values into your expression and add it up. Presto all done.

Answer 20

my number seems really off.. i got -463/150

Answer 21

i got the 9/25 but then it has to be multiplied by 3 right, according to the expression

Answer 22

find 5tant-2csct+cos^2^t
is what you typed in.

Answer 23

oh im sorry its 5tant-2csct+3cos^2^t

Answer 24

tan(t)= -4/3
csc(t)= -5/4
cos^2(t)= 9/25
5tan(t)-2csc(t)+3cos^2(t)

-20/3 + 10/4 + 27/25= (-2000 +750 + 324)/300= -926/300= -463/150

Answer 25

whew! ok i thought i did something wrong (besides write the problem incorrectly) thank u!!