1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof of inverse trigonometric identities

  1. Aug 14, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that arcsin(1/sqrt(5)) + arcsine(2/sqrt(5)) = Pi/2

    2. Relevant equations

    3. The attempt at a solution

    Can someone please give me so much as a hint?
  2. jcsd
  3. Aug 14, 2011 #2


    User Avatar
    Homework Helper

    Take the sine of the left-hand side and see if it is equal to sin(pi/2)

  4. Aug 14, 2011 #3


    User Avatar
    Homework Helper

    Look at each term individually. Each is the arcsine of a ratio, so each term is an angle.

    For the first term, if theta = arcsin(1/√5) , then sin(theta) = 1/√5 . Draw a right triangle with one angle being (theta) and having the side opposite (theta) equal to 1 and the hypotenuse equal to √5 . What is the side adjacent to (theta) equal to?

    Now, is there an angle in that triangle having a sine of 2/√5 ? If so, it would be an angle which is the arcsine of (2/√5) . Call it (phi) . What do (theta) and (phi) add up to?
  5. Aug 14, 2011 #4


    User Avatar
    Homework Helper

    Draw a triangle and use pythagorus. [Just hints, not answers]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Proof of inverse trigonometric identities
  1. Trigonometric identity (Replies: 1)

  2. Trigonometric identity (Replies: 7)

  3. Trigonometric Identity (Replies: 1)