Trig

posted by .

Find the exact values of sin 2 theta, cos 2 theta and tan 2thea using the double angle formula
sin theta = 3/4 , pi/2 < theta < pi

  • Trig -

    given: sinØ = 3/4, and Ø is in quadrant II
    then by Pythagoras, y= 3, x = ? , r = 4
    x^2 + 9 = 16
    x = ±√5 , but in II x = -√7
    so cosØ = -√7/4

    sin 2Ø = 2sinØcosØ
    = 2(3/4)(-√7/4) = -6√7/16
    = -3√7/8

    cos 2Ø = cos^2 Ø - sin^2 Ø = 7/16 - 9/16
    = -2/16
    = - 1/8


    tan 2Ø = sin 2Ø / cos 2Ø
    = (-3√7/8) / (-1/8)
    = 3√7

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. simple trig

    If sin(theta)=[sqrt(70)]/7 and theta is in Quadrant two, find the exact numerical value of tan theta without using a calculator. I got tan(theta)=[sqrt(294)]/42 Is that right?
  2. easy trig

    If sin(theta)=[sqrt(70)]/7 and theta is in Quadrant two, find the exact numerical value of tan theta without using a calculator. I got tan(theta)=[sqrt(294)]/42 Is that right?
  3. 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 …
  4. trig

    the terminal side of angle theta in standard position lies on the line that travels through point (9,1), find sin of theta, cos of theta, tan of theta. (give exact values)
  5. Math

    1. Let (-7, 4) be a point on the terminal side of (theta). Find the exact values of sin(theta), csc(theta), and cot(theta). 2. Let (theta) be an angle in quadrant IV such that sin(theta)=-2/5. Find the exact values of sec(theta) and …
  6. Trig

    1. Establish the identity: sin(theta+3pi/2)=-cos(theta) 2. Find the exact value of 2(theta) if sin(theta)=5/13 3. Show that: csc2(theta)-cot2(theta)=tan(theta) 4. Find the exact value of tan(cos^-1(square root of 3/2) 5. Approximate …
  7. 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.
  8. trig

    Find csc(theta), tan (theta), and cos (theta), where theta is the angle shown in the figure. Give exact values, not decimal approximations c=10 b=7 a=7.14 the right angle is locate between sides a and b and the theta angle is an acutle …
  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. 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 …

More Similar Questions