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).

  1. 👍 0
  2. 👎 0
  3. 👁 2,323
  1. sin^2 + cos^2 = 1 ... cos = √(1 - sin^2) = √[1 - (-2/5)^2]

    find the cosine ... remember, it's positive in Quad IV

    sec = 1 / cos ... tan = sin / cos

    1. 👍 0
    2. 👎 0
  2. in QIV, x is positive and y is negative. So, if sinθ = -2/5, you have

    y = -2
    r = 5
    x = √21

    Now, recall that
    sinθ = y/r
    cosθ = x/r
    tanθ = y/x
    and of course, there are the reciprocals: csc, sec, cot

    1. 👍 0
    2. 👎 0
  3. Y = -2.
    r = 5.
    x^2 + (-2)^2 = 5^2,
    X = sqrt(21).

    Sec A = 1/Cos A = 1 / (x/r) = r/x = 5/sqrt(21).
    Tan A = Y/X = -2/sqrt(21).

    1. 👍 0
    2. 👎 0

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. 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?

  3. 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?

  4. 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?

  1. 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

  2. Maths: Partial Differentiation

    1) If x = rcos theta and y = r sin theta, show that partial r / partial x = cos theta and find partial theta / partial x. 2) If z = sin theta.sin phi.sin gamma, and z is calculated for the values theta = 30degrees, phi = 45

  3. trig

    Let (theta) be an angle in quadrant II such that csc(theta)=8/5 Find the exact value of tan(theta) and cos(theta).

  4. Trig(3 all with work)

    1)Find the exact value of cos 105 by using a half-angle formula. A)sqrt 2 - sqrt 3 /2 B)-sqrt 2 - sqrt 3 /2 C)-sqrt 2 + sqrt 3 /2 D)sqrt 2 + sqrt 3 /2 cos 105 cos 105 = cos 210/2 sqrt 1 + 210/2 sqrt 1 + sqrt 3/2 /2 sqrt 2 + sqrt

  1. Precalculus check answers help!

    1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.)

  2. Pre-Calculus-check answers

    If cos theta = 0.8 and 270

  3. 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.

  4. Trigonometry

    State the quadrant in which theta lies. sin(theta) > 0 and cos(theta) > 0 How can I determine this? Please explain.

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