SOLUTION: If 0 < p < pi/2 and x=6sin p, what is tan p for the indicated trigonometric function: {{{ sqrt(36-x^2) }}}? I have used identities to work the problem down to 6cos p, but I am n

Algebra ->  Trigonometry-basics -> SOLUTION: If 0 < p < pi/2 and x=6sin p, what is tan p for the indicated trigonometric function: {{{ sqrt(36-x^2) }}}? I have used identities to work the problem down to 6cos p, but I am n      Log On


   

Question 762930: If 0 < p < pi/2 and x=6sin p, what is tan p for the indicated trigonometric function: +sqrt%2836-x%5E2%29+?
I have used identities to work the problem down to 6cos p, but I am not sure how to get tangent from that answer. I need your help, please!
Thank you!!
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
I'm with you, I did the same thing, but let's look at it differently. Draw a right triangle with one of the angles with a measure of p degrees. Note p is between 0 and 90 degrees. Now we are given
(1) x = 6sin(p) or
(2) sin(p) = x/6
The side opposite p is x and the hypotheneus is 6. The other side is
(3) sqrt%286%5E2+-+x%5E2%29
Therefore the tangent of p is
(4) tan%28p%29+=+x%2F%28sqrt%286%5E2+-+x%5E2%29%29
To check this substitute (1) into (4) and get
(5) tan%28p%29+=+%286sin%28p%29%29%2F%28sqrt%2836+-+36sin%28p%29%5E2%29%29 or
(6) tan%28p%29+=+%286sin%28p%29%29%2F%286sqrt%281+-+sin%28p%29%5E2%29%29 or
(7) tan%28p%29+=+sin%28p%29%2F%28sqrt%28cos%28p%29%5E2%29%29 or
(8) tan%28p%29+=+sin%28p%29%2Fcos%28p%29 QED
Answer: tan%28p%29+=+x%2F%28sqrt%286%5E2+-+x%5E2%29%29