Expert: Paul Klarreich - 6/20/2009

Question
Hi myy name's Veronica and I'm currently having trouble
answering these problems. I believe they have to be verified
using the pythagorean identities (i think) but my notes are
only about the sin, cos, tan, etc. I dont have notes about
these kind of problems. Please help me. Thanks.

Problems:

1) Verify: sin(theta)cos(theta)=x(square root of 25-x^2) all
over 25. where theta is an acute angle of triangle ABC withe
one side x.

2) tan^2A=x^2 all over 9-x^2

3) 4sin^2A over cosA= x^2 all over square root of 16-x^2

I will Be waiting for your answers.. Please help me I would
greatly appreciate it.. Thanks again.

Answer
Questioner:   Veronica
Country:  Philippines
Category:  Calculus
Private:  No
 
Subject:  TRIGONOMETRY (trigonometric functions) but not sure if this is also included with it
Question:  Hi my name's Veronica and I'm currently having trouble
answering these problems. I believe they have to be verified
using the pythagorean identities (i think)

>> and the quotient identities and the reciprocal identities, etc. -- you have to know them all.

but my notes are only about the sin, cos, tan, etc. I dont have notes about
these kind of problems. Please help me. Thanks.

Problems:

1) Verify: sin(theta)cos(theta)=x(square root of 25-x^2) all
over 25. where theta is an acute angle of triangle ABC withe
one side x.

2) tan^2A=x^2 all over 9-x^2

3) 4sin^2A over cosA= x^2 all over square root of 16-x^2

I will Be waiting for your answers.. Please help me I would
greatly appreciate it.. Thanks again.
..........................................................
Hi, Veronica,

I think you have left out some information in each of these, such as a 'beginning' value of one of the functions or the dimensions of the triangle.

1) Verify: sin(t) cos(t)= x sqrt(25-x^2) /25.
over 25. where theta is an acute angle of triangle ABC withe
one side x.  

YOU MEAN with one side x that is opposite angle t, and the hypotenuse equal to 5, don't you.  Your triangle looks like this:
         B
        /|
       / |
      /  |
     /   |
  5 /    | x
   /     |
  /      |
 /       |
/ t      |
A---------+C
sqrt(25 - x^2)

and you got AC by using the Pythagorean Theorem.  Now it is an easy matter to write:
          x  
sin t = -------
          5

             x  
cos t = --------------
       sqrt(25 - x^2)


and now you can verify your identity.

I think that you can now go back and handle the other problems.  You will supply the missing information and do them the same way.