Trigonometry

posted by .

If cot 2(Theta) = 5/12 with 0 (less than or equal to) 2(Theta) (Less than or equal to) Pi, find the cos(Theta), sin(Theta), and tan(Theta).

  • Trigonometry -

    cot(2A) = X/Y = 5/12. Q1.
    r^2 = 5^2 + 12^2 = 169
    r = 13.

    cos(2A) = X/r = 5/13.
    sin(2A) = Y/r = 12/13.
    tan(2A) = Y/X = 12/5.

    cos2A = 2cos^2A-1 = 5/13
    2cos^2A = 5/13 + 1 = 18/13
    cos^2A = 18/26
    cosA = sqrt(18/26)
    cosA = 3sqrt(2/26)
    cosA = 3*sqrt(1/13).
    sqrt = Square root.

    sin(2A) = 2sinA*cosA = 12/13.
    2sinA*3sqrt(1/13) = 12/13
    sinA*3sqrt(1/13) = 12/26
    sinA = (12/26)/(3sqrt(1/13)
    sinA = (4/26)/(sqrt(1/13)
    sinA = (2/13)/(sqrt(1/13)
    sinA = (2/13)sqrt(1/13)/(1/13)
    sinA = 2sqrt(1/13).

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra II

    Which of the following expressions are not equal to 1?
  2. Calculus

    I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure …
  3. Algebra II

    Multiple Choice Which expression is NOT equivalent to 1?
  4. trig

    If tan theta = sin theta, and theta is greater than or equal to 0 and less than or equal to 2 pi. find cos theta and what is theta
  5. Trigonometry

    Thank you STEVE!!!!! Suppose that Cos (theta) = 1/square root 2 if 0<equal to theta , pi/2 then sin(theta) = tan (theta) = If 3pi/2 less than equal to theta , 2pi then sin(theta) = tan (theta) = I know the trig functions but I feel …
  6. trig

    If sin theta is equal to 5/13 and theta is an angle in quadrant II find the value of cos theta, sec theta, tan theta, csc theta, cot theta.
  7. Math Trig Help

    sin theta = x/3, with theta in the first quadrant, find the expression for cos theta and tan theta. Answers will be in algebraic terms of x. Give exact answers with 0 < theta <pi/2 (0 less than or equal to theta, less than or …
  8. Trigonometry

    Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
  9. Trigonometry

    Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
  10. Precalculus

    Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the segment …

More Similar Questions