what is tan(sin^-1(3/7)+cos^-1(4/5))?

Question

I get confused when I have to do the tangent part of the equation.

Answer 1

Likely the expectation is for you to use the identity for the tangent of the sum of two angles.

 

tan(x+y) = (tan x + tan y)/(1-tanxtany).

 

In this case x = arc sin(3/7) and y = arc cos 4/5. 

 

To find the tangent of x and tangent of y there are a few ways to proceed. One way is to draw a little right triangle (placing the 3 and 7 as opp and hypotenuse respectively, find the adjacent side using the Pythagorean theorem which then allows you to find the tangent. For example tan x = 3/√40. Find tan y too and substitute into the identity.

 

Check this graph for a possible answer:

 

https://www.desmos.com/calculator/lpiakqx3xf

 

You could rationalize the denominator to get a different format for the exact answer.