mathematics

posted by .

given sinθ=-5/13 and π<θ<3π/2 find

sin2θ
cos( θ-4π/3)
sin(θ/2)

can some1 please help me with this?

  • mathematics -

    Let's go through this again.
    θ is in the 3rd quadrant, so x and y are both negative, and the hypotenuse h = 13

    sinθ = -5/13
    cosθ = -12/13

    Use these values in your half-angle and double-angle and sum/difference formulas.

    sin 2θ = 2 sinθ cosθ = 2(-5/13)(-12/13) = 120/169

    cos(θ-4π/3) = cosθ cos4π/3 + sinθ sin4π/3
    = (-12/13)(-1/2) + (-5/13)(-√3/2)
    = 12/26 + 5√3/26

    sin θ/2 = √((1-cosθ)/2)
    = √((1 + 12/13)/2)
    = √(25/26)


    Use this same method for all your other similar problems.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math - Calculus

    The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below. | a …
  2. trig

    cosθ =5/13 with -π/2 < θ <0 find each of the following sin( θ - 5π/4) cos( θ - 11π/6) tan( θ + 5π/4) can some1 explain to me how to do these?
  3. trigonometry

    tanθ= -2sqrt10/3 and π/2<θ< π find a. cos(-θ) b. cos(11π/6 - θ) c.sin2θ d.tanθ/2 can some please explain to me how to solve these questions?
  4. math

    given sinθ=-5/13 and π<θ<3π/2 find sin2θ cos( θ-4π/3) sin(θ/2) can some1 explain to me how to do these?
  5. math

    if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me?
  6. trigonometry

    given tanθ= -2√10/3 and π/2<θ< π find: sin2θ tan θ/2 given sinθ=-5/13 and π<θ<3π/2 find sin2θ cos( θ-4π/3) sin(θ/2) can some1 explain this to me …
  7. trigonometry

    if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5π/3) sin2θ cos2θ cos(θ/2) can some1 please help me?
  8. mathematics

    given tanθ= -2√10/3 and π/2<θ< π find: a.sin2θ b.tan θ/2 could some1 help me with these 2 they're the only ones i couldn't get
  9. TRIGONOMETRY

    Can you check my work, please? This is for a trig study guide for my final next week. I'd like to know if I'm doing this right. :) 2. The polar coordinates of a point are given. Find the rectangular coordinates of each point. a. (5,(π
  10. Precalc/Trig

    Sorry there are quite a few problems, but I just need to know if these are correct (and if they aren't, where I went wrong): 1. Solve these equations. tanθ = -√3 θ = 2π/3 + kπ θ = 5π/3 + kπ …

More Similar Questions