Trigonometry
posted by Elena .
find sin2x, cos2x, and tan2x if sinx= 2/sqrt 5 and x terminates in quadrant III

Trigonometry 
Reiny
if sinx = 2/√5 in III
y = 2, r = √5 , by Pythagoras,
x^2 + 4 = 5
x = 1 in III
cosx = 1/√5
tanx = sinx/cosx = (2/√)/(1/√5) = 2
sin 2x = 2sinxcosx = 2(2/√5)(1/√5) = 4/5
cos 2x = cos^2 x  sin^2 x = 1/5  4/5 = 3/5
tan 2x
= 2tanx/(1  tan^2 x)
=2(2)/(1  4) = 4/3
Respond to this Question
Similar Questions

trig
sinx = 4/5 and x terminates in Quadrant II Find sin2x and cos2x How to get the answers, which are sin2x = 24/25, cos2x = 7/25? 
Trigonometry
I can't remember what formula to use for these. Note the X's may be replaced by a theta symbol. I just didn't have one on my keyboard. Use the given information to find sin2X, cos2X and tan2X if 0< X <pi/2 1. sinX=12/13 2. cosX=3/5 … 
trig
Verify the trigonometric identity: [(1–sin²x)/sin²x]–[(csc²x–1)/cos²x]= tan²x I can't figure this out. 
Precalculus
If sinx= 1/4 and x terminates in the third quadrant, find the exact value of sin2x My answer is sqrt15/8 
Trig
Prove the following functions: (sinx+sin2x)/(1+cosx+cos2x)=tan x (cos3x/sinx)+(sin3x/cosx)=2cot2x tan2x=(2/cotxtanx) theses are due in the am. Fastness would be great? 
precalculus
tanx= 12/5 x in quadrant 2 find; sin2x= cos2x= tan2x= 
Trig
help please!: (sinx + sin2x +sin3x) / (cosx + cos2x + cos3x) = tan2x 
Math please help quick
Which of the following are identities? Check all that apply. (Points : 2) sin2x = 1  cos2x sin2x  cos2x = 1 tan2x = 1 + sec2x cot2x = csc2x  1 Question 4. 4. Which of the following equations are identities? 
PreCalculus
If sinx=1/2 and x terminates in the third quadrant, find the exact value of tan2x. 
math
sin2x − cos2x − tan2x = 2sin2x − 2sin4x − 1/ 1 − sin2x for x = 45