Trig

posted by .

given sin(4x)=5/13 in Q II

find Tan(2x) and cos(2x)

  • Trig -

    sin 4 x = 5/13
    then cos 4 x = 12/13 (5,12,13 right triangle)
    and
    tan 4x = sin 4 x /cos 4x = 5/12
    so identities:
    sin 4x = 2 sin 2x cos 2x = 5/13
    cos 4x = cos^2 2x - sin^2 2x = 12/13
    tan 4x = 2 tan 2x / (1-tan^2 2x) = 5/12

    so
    cos^2 2x = 12/13 + sin^2 2x
    = 12/13 + [ 5/(26 cos 2x)]^2
    = 12/13 + 25 /(114244 cos^2 2x)
    114244 cos^4 2x = 105456 cos^2 2x + 25
    cos^4 2x - .9231 cos^2 2x - .00021883=0
    cos^2 2x = (1/2)[.9231 +/- .96124]
    cos^2 2x =.4616 +/- .4806
    use + sign
    cos^2 2x = .94217
    cos 2x = .9707
    check my arithmetic then go on and get the sin 2x and tan 2x

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Trig

    Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
  2. Mathematics - Trigonometric Identities

    Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y …
  3. TRIG!

    Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
  4. trig 26

    simplify to a constant or trig func. 1. sec ²u-tan ²u/cos ²v+sin ²v change expression to only sines and cosines. then to a basic trig function. 2. sin(theta) - tan(theta)*cos(theta)+ cos(pi/2 - theta) 3. (sec y - tan y)(sec y + …
  5. TRIG

    what is another form of: sin (A+B) sin (A-B)/ cos^2 A cos^2 B a) cos^2 A - cos^2 B b) tan^2 A - tan^2 B c) tan^2 A - tan^2 B d) sin^2 A - sin^2 B please show the steps you take to get to the answer! thank you
  6. Trigonometry

    Please review and tell me if i did something wrong. Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot 19degrees …
  7. Trigonometry

    1.Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two decimal places. 6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin y 10.Prove that 1+tanθ/1-tanθ = sec^2θ+2tanθ/1-tan^2θ 17.Prove that …
  8. Trig Identities

    Proving identities: 1) 1+ 1/tan^2x = 1/sin^2x 2) 2sin^2 x-1 = sin^2x - cos^2x 3) 1/cosx - cosx = sin x tan x 4) sin x + tan x =tan x (1+cos x) 5) 1/1-sin^2x= 1+tan^2 x How in the world do I prove this...please help... I appreciateyour …
  9. precalculus

    For each of the following determine whether or not it is an identity and prove your result. a. cos(x)sec(x)-sin^2(x)=cos^2(x) b. tan(x+(pi/4))= (tan(x)+1)/(1-tan(x)) c. (cos(x+y))/(cos(x-y))= (1-tan(x)tan(y))/(1+tan(x)tan(y)) d. (tan(x)+sin(x))/(1+cos(x))=tan(x) …
  10. Pre-calculus help

    I have two problems I am stuck on, if you could show me how to solve the problems it would be much appreciated. 1) Find sin 2x, cos 2x, and tan 2x from the given information. tan x = − 1/6, cos x > 0 sin 2x = cos 2x = tan …

More Similar Questions