trigonometry

3. write tan (π/4-β) as a function of β only.

8. write cos(λ+ π/3) as a function of λ only.


16. Write cos(–83°) as a function of a positive angle.

23. Write sin(125°) in terms of its cofunction. Make sure your answer is a function of a positive angle.

31. Find the exact value of sin(195°).

  1. 👍 0
  2. 👎 0
  3. 👁 54
asked by yoshi
  1. 3.
    tan (π/4-β) = (tanπ/4 - tanβ)/(1+tanπ/4 * tanβ) = (1-tanβ)/(1+tanβ)

    8.
    cos(λ+ π/3) = cosλ cosπ/3 - sinλ sinπ/3
    = 1/2 cosλ - √3/2 sinλ

    16.
    Since cos(-x) = cos(x),
    cos(-83°) = cos(83°)

    23.
    sin(x) = cos(90°-x), so
    sin(125°) = cos(90°-125°) = cos(-35°) = cos(35°)

    31.
    sin(195°) = sin(180°+15°) = -sin(15°) = -sin(30°/2)
    = -√((1-cos(30°))/2)
    = -√(1-√3/2)/2)
    = -√(2-√3) / 2 = -(√3-1) / 2√2

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. trig help much appreciated! :))

    1. Find the complete exact solution of sin x = . 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. 4. Prove

    asked by suzy on August 16, 2013
  2. Math

    Write the first trigonometric function in terms of the second for θ in the given quadrant. tan(θ), cos(θ); θ in Quadrant IV I believe to start this is 1/cos^2*theta. Am I write? If not, can you please help me?!

    asked by Jennifer on April 14, 2016
  3. Math

    This one confused me since it revolved around what seemed like dividing trig function by another function Write the following expression in terms of the tangent function 2 / ((cos(r^2 - s^2) / (sin(r^2 - s^2)) = ? I know tan t =

    asked by Taylor on November 14, 2014
  4. Pre-Calc

    I am really struggling with how to do these problems, I posted them a few minutes ago but the answers/work shown was incorrect. 1) a) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of

    asked by Alyssa on April 13, 2015
  5. Trigonometry

    Write cos(-83degrees) as a function of a positive angle Prove that tan^2(alpha)-1+cos^2(alpha)=tan^2(alpha)sin^2(alpha)

    asked by Anonymous on August 12, 2012
  6. Maths- complex numbers

    Find tan(3 theta) in terms of tan theta Use the formula tan (a + b) = (tan a + tan b)/[1 - tan a tan b) in two steps. First, let a = b = theta and get a formula for tan (2 theta). tan (2 theta) = 2 tan theta/[(1 - tan theta)^2]

    asked by Jake on February 13, 2007
  7. trig 26

    simplify to a constant or trig func. 1. sec ²u-tan ²u/cos ²v+sin ²v change expression to only sines and cosines. then to a basic trig function. 2. sin(theta) - tan(theta)*cos(theta)+ cos(pi/2 - theta) 3. (sec y - tan y)(sec y

    asked by hilde on March 14, 2010
  8. Pre-Calc

    1) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. cos 12° cos 18° − sin 12° sin 18° And Find its exact value. 2) Use an Addition or Subtraction Formula to write the

    asked by Alyssa on April 13, 2015
  9. Trig.

    sec^2xcotx-cotx=tanx (1/cos)^2 times (1/tan)-(1/tan)=tan (1/cos^2) times (-2/tan)=tan (-2/cos^2tan)times tan=tan(tan) sq. root of (-2/cos^2)= sq. root of (tan^2) sq. root of (2i)/cos=tan I'm not sure if I did this right. If I

    asked by Trig on January 9, 2010
  10. Trig

    Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos v + cos v

    asked by Nan on December 29, 2006

More Similar Questions