trig

Find the exact value of costheta if ,sintheta=-2/3 and theta is in standard position with its terminal side in Quadrant IV.

  1. 👍
  2. 👎
  3. 👁
  1. cos θ = ± √ ( 1 - sin² θ )

    In quadrant IV sine is negative , cosine is positive.

    So in quadrant IV cos θ = √ ( 1 - sin² θ )

    In this case:

    cos θ = √ ( 1 - sin² θ ) = √ [ 1 - ( - 2 / 3 )² ] = √ ( 1 - 4 / 9 ) =

    √ ( 9 / 9 - 4 / 9 ) = √ ( 5 / 9 ) = √ 5 / √ 9 = √ 5 / 3

    1. 👍
    2. 👎
  2. in QIV,
    y = -2
    r = 3
    x = √5

    cosθ = x/r = √5/3

    1. 👍
    2. 👎
  3. MMMMM

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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)

  2. Physics

    One end of a uniform meter stick is placed against a vertical wall. The other end is held by a lightweight cord that makes an angle, theta, with the stick. The coefficient of static friction between the end of the meter stick and

  3. Trigonometry

    Let (7,-3) be a point on the terminal side of theta. Find the exact values of cos of theta, sec of theta and cot of theta?

  4. Math

    Suppose theta is an angle in standard position with cos theta > 0. In which quadrants could the terminal side of theta lie? Select two answers. I II III IV I don't know what this means:(

  1. calculus

    let theta be an angle of quadrant IV such that sin theta = -8/9 find the exact value of sec theta and cot theta?

  2. Math

    Let (7,-3) be a point on the terminal side of theta. Find the exact values of sin of theta, csc of theta and cot of theta?

  3. 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

  4. trig

    the terminal side of an angle theta in standard position coincides with the line y=5x and lies in quadrant 3. find the six trigonometric functions of theta.

  1. Math

    Find the value of csc theta for angle theta in standard position if the point at (5,-2) lies on its terminal side.

  2. math

    Let theta be an angle in quadrant IV such that sin(theta)=-(2)/(5). Find the exact values of sec(theta) and tan(theta).

  3. Trigonometry

    Point P is located at the intersection of the unit circle and the terminal side of angle theta in standard position. Find the coordinates of P to the nearest thousandth. theta = -105degrees Please explain the steps. I'm completely

  4. Algebra 2

    Find the exact values of the six trigonometric functions of theta if the terminal side of theta in standard position contains the point (-5/-4)

You can view more similar questions or ask a new question.