SOLUTION: tan(sin^-1(1/7))

Algebra.Com
Question 1094706: tan(sin^-1(1/7))
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20066)   (Show Source): You can put this solution on YOUR website!


First we look at the inner part: 

That asks for the angle between  and  whose sine
is .  

Since we know that ,
we draw such an angle by placing a right triangle
in the first quadrant whose angle at the origin is such that its
opposite side is y=1 and its hypotenuse is r=7, like this:



The angle indicated by the red arc is the angle: .

To find the tangent, we must calculate the adjacent side x,
using the Pythagorean theorem:









So we now have all three sides of the right triangle:



The problem is 



and since we know that 

.

Edwin


Answer by ikleyn(52931)   (Show Source): You can put this solution on YOUR website!
.
tan(sin^-1(1/7))
~~~~~~~~~~~~~~~~~~~

  is  .


So,  they want you calculate  ,  where  = .


Since   = ,  it means that   = .


Then   =  =  =  =  =  = .


Finally,    =  =  =  = .


For many other similar solved problems, see the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
    - Evaluating trigonometric expressions

    - OVERVIEW of lessons on calculating trig functions and solving trig equations
in this site.


RELATED QUESTIONS

tan... (answered by ikleyn)
tan(sin^-1 3/4-cox^-1... (answered by DrBeeee)
tan(sin^-1(3/5)) (answered by lwsshak3)
Tan(sin^-1(-3/8) (answered by ikleyn)
Sin-1 (tan... (answered by Alan3354)
sin^-1{{{ sqrt( 3 ) /2 ) }}} cos^-1{{{-sqrt( 3 ) /2) }}} tan^-1(-1)... (answered by stanbon)
sin (x + y)/ sin (x - y) = tan(x) + tan(y) / 1 + tan(x)tan(y) (answered by Alan3354)
Evaluate exactly:... (answered by MathLover1)
sin-cos+1 / sin + cos-1=... (answered by Alan3354)