Trig (inverse functions)

tan[arccsc(-5/3) + arctan(1/4)]

My work:
let arccsc(-5/3)=X and let arctan(1/4)=Y
where -pi/2<=X<=pi/2, X cannot be 0
and where -pi/2<Y<pi/2
so that cscX=-5/3 and tanY=1/4

The problem can now be written as
=tanX + tanY/1-tanXtanY which could also be written as
=sinXcosY + cosXsinY/cosXcosY - sinXsinY

I drew the respective triangles and came up with (for the X triangle) a=4, b=-3, c=5. (for the Y triangle) a=1, b=4,c=sqrt17

so sinX=-3/5 cosX=4/5
sinY=4/sqrt17 cosY=1/sqrt17

=[(-3/5)(1/sqrt17) + (4/5)(4/sqrt17)]/[(4/5)(1/sqrt17)-(-3/5)(4/sqrt17)]


This is not the correct answer. The book shows an answer of -8/19

Can someone please tell me where I went wrong. You don't have to give me the whole working, just where I started to go wrong.

Thank you so much. (hopefully all that typed stuff makes sense, it's hard without being able to use mathematical characters)

asked by Dennis
  1. I found my mistake, please disregard.

    posted by Dennis

Respond to this Question

First Name

Your Response

Similar Questions

  1. adv functions

    Show that tanx= (sinx/ cosx) can be written as: tan(x-y) = (tanx - tany) / (1+ tanxtany)
  2. advanced functions

    Show that tanx = sinx / cosx can be written as tan(x+y) = (tanx + tany) / (1 - tanxtany)
  3. trigonometry (please double check this)

    Solve the following trig equations. give all the positive values of the angle between 0 degrees and 360 degrees that will satisfy each. give any approximate value to the nearest minute only. a.) ( I got confused doing this 1 can
  4. solving trigonometrical equations

    arctan(tan(2pi/3) thanks. arctan(tan(2pi/3) = -pi/3 since arctan and tan are inverse operations, the solution would be 2pi/3 the number of solutions to arctan(x) is infinite, look at its graph. generally, unless a general solution
  5. Trig

    If tanx = 2/3 tany = 1/2 then tan(x-y) = ?? a.7/4 b.7/6 c.1/8 d.8/6 which answer is correct ??
  6. Calculus

    Okay so I have a question on my assignment that says: You are given that tan(y) = x. Find sin(y)^2. Express your answer in terms of x. I know its derivatives, and I've tried taking the derivatives of both etc, and got them both to
  7. End behavior models

    Thanks for the help with my previous problems Roger & Leo. It was really helpful. Now I want to know how to find the right and left end behavior models and horizontal tangents for the inverse functions, say y = tan inverse(x) I
  8. limiting position of the particle

    A particle moves along the x axis so that its position at any time t>= 0 is given by x = arctan t What is the limiting position of the particle as t approaches infinity? Answer is pi/2 How do I solve this? Thanks a lot. You
  9. Math

    Arrange these in order from least to greatest: arctan(-sqrt3), arctan 0, arctan(1/2) So far I got the first two values, arctan(-sqrt3), and that's 150 degrees. Arctan 0 would be zero degrees. I'll use just one answer for now, but
  10. calculus

    Let f be a function defined by f(x)= arctan x/2 + arctan x. the value of f'(0) is? It's 3/2 but I am not very clear on how to obtain the answer. I changed arctan x/2 into dy/dx=(4-2x)/(4sqrt(4+x^2)) but that's as far as I got.

More Similar Questions