math

posted by .

tan theta= 15/8 and pi< theta<3pi/2

a. Sin(- theta)
b. cos2theta
c. sin( theta - 3pi/4)
d. cos(theta/2)

can someone explain to me how do you find the exact value for these?

  • math -

    the angle is in the 3rd quadrant.
    So, draw a diagram where the hypotenuse extends down to the left from (0,0)

    Since tan = y/x, this means that y = -15 and x = -8. So the hypotenuse of your triangle goes from (0,0) to (-8,-15), length=17

    Now you are ready to go.

    sin theta = y/h = -15/17
    cos theta = x/h = -8/17

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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  2. Precalculus(NEED HELP ASAP PLEASE!!)

    cot(theta)= 3 pi < theta < 3pi/2 Find: sin(theta)= -1 ?
  3. 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 …
  4. 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 …
  5. 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.) Simplify …
  6. 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.) Simplify …
  7. 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 …
  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. Algebra 2

    What values for theta(0 <= theta <= 2pi) satisfy the equation?

More Similar Questions