If X = 2/3, 180 degree < X< 270 degree, how do i find the exact values for:?

Question

a. tan 2X

b. cos 2X

c. sin 2X

I'm unable to figure out how the answer key came up with th e following answers: a. 12/5 , b. -5/13, c. -12/13
Please show me why these answers are correct.

Answer 1

you seem to have made some mistake while posting the question

Answer 2

u should b knowing the 4 quadrants v use in coordinate geometry.
1st quadrant=0 to 90 degree-In this quadrant,all ratios r positive
2nd=90 to 180 degree-In this quadrant,Sin is positive
3rd=180 to 270 degree-In this quadrant, Tan is positive
4th=270 to 360 degree-In this quadrant, Cos is positive

So,in ur Q,u refer to the 3rd quadrant.
Tan is positive,Cos ,Sin r negative.
though i can answer the sign convention problem,i think the data u gave is incrrect.What is x=2/3 ?and who told u 2/3=0.666 lies between 180degree and 270 degree?please check with ur data.The rest of the problem can b solved using Pythagoras Theorem, given the right data.

Answer 3

Please clarify the question. If X = 2/3, how can it also be between 180 degrees and 270 degrees? Even if 2/3 is radians instead of degrees it still doesn't work.