Pre-Cal

Find sin 2x, cos 2x, and tan 2x from the given information.

[1]. sin x = 8/17, x in Quadrant I

1). sin 2x =________.

2). cos 2x =________.

3). tan 2x =________.


[2]. sin x = -5/13, x in Quadrant III

1). sin 2x =________.

2). cos 2x =________.

3). tan 2x =________.


[Note: I'm having a lot of trouble with these. From what I'm told the answers are suppose to come in fraction forms]

  1. 👍 0
  2. 👎 0
  3. 👁 545
asked by Amber
  1. sinx = 8/17
    so, cosx = 15/7

    sin2x = 2 sinx cosx = 2 * 8/7 * 15/7 = 240/49

    do the others similarly.

    1. 👍 0
    2. 👎 0
    posted by Steve
  2. oops

    sinx = 8/17
    so, cosx = 15/17

    sin2x = 2 sinx cosx = 2 * 8/17 * 15/17 = 240/289

    1. 👍 1
    2. 👎 0
    posted by Steve
  3. I will do the 2nd one, which is the harder of the two.
    Follow my steps to do the first one.

    sinx = -5/13 ,and the angle x is in III
    recall that sinØ = y/r
    so y = -5, r = 13
    sketch a right-angled triangle in III with hypotenuse 13 and y = -5
    x^2 + y^2 = r^2
    x^2 + 25 =169
    x^2 = 144
    x = ± 12 , but we are in III, so x = -12

    giving us cosx = -12/13

    recall that sin 2x = 2sinx cosx
    = 2(-5/13)(-12/13)
    = 120/169

    recall cos 2x = cos^2 x - sin^2 x
    = 144/169 - 25/169
    = 119/169

    recall tan 2x = sin2x/cos2x
    = (120/169) / (119/169)
    = 120/119

    1. 👍 0
    2. 👎 1
    posted by Reiny

Respond to this Question

First Name

Your Response

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 v + cos v

    asked by Nan on December 29, 2006
  2. 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

    asked by Anon on January 1, 2011
  3. 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) =

    asked by Anonymous on November 8, 2007
  4. 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 +

    asked by hayden on February 23, 2009
  5. 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 2x =

    asked by Holly on April 10, 2015
  6. Math

    Evaluate *Note - We have to find the exact value of these. That I know to do. For example sin5π/12 will be broken into sin (π/6) + (π/4) So... sin 5π/12 sin (π/6) + (π/4) sin π/6 cos π/4 + cos π/6 sin π/4 I get all those

    asked by Anonymous on November 25, 2007
  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 sin^2w-cos^2w/tan

    asked by Alonso on January 1, 2013
  8. 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.

    asked by anonymous on April 14, 2013
  9. Precalculus

    I am trying to submit this homework in but i guess i'm not doing it in exact values because it is not accepting it. I know i'm supposed to be using half angle formulas but maybe the quadrants are messing me up. Please help! Find

    asked by J.P. on November 9, 2015
  10. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

    asked by Pablo on November 26, 2006

More Similar Questions