Consider the expression tan 2 sin135 a Fill in the blanks Le

Consider the expression: tan (2 sin^-1(3/5)) a) Fill in the blanks: Let ________ = theta where theta belongsto [__, __]. Then _____ = 3/5. b) Now, WITHOUT using a calculator, use part a to find the EXACT value of the expression. If it is undefined, so state and explain why. (Must SHOW ALL the correct algebraic steps for credit. No decimals!)

Solution

tan ( 2 sin^-1 ( 3/5 ))

let

theta = sin^-1 (3/5)

sin theta = 3/5

tan ( 2 theta ) = 2 tan theta / ( 1 - tan^2 theta )

tan theta = 3 / 4

tan ( 2 theta ) = 2 (3/4) / 1 - (3/4)^2 = 6/4 / ( 1 - 9/16)

tan ( 2 sin^-1 ( 3/5 )) = 24 / 7