SAT Math IIC Trig Problem: If [tan(x)-1]^2=4 then which...?

[vortex705]

If [tan(x)-1]^2=4 then which of the following could be the value of x in radian measure?
A. -.0785
B. 1.373
C. 1.504
D. 1.512
E. 3

I guess i can just plug it into the calculator using solve function, but can you please show me how to solve this problem? when i plugged into my TI, the answer i got was A.

 

[soroban]

Re: SAT Math IIC TRIG PROBLEM

Hello, vortex705!

If \(\displaystyle (\tan x-1)^2\:=\:4\), then which of the following could be the value of \(\displaystyle x\) in radian measure?

. . \(\displaystyle (A)\;\text{-}0.0785\qquad(B)\;1.373\qquad(C)\;1.504 \qquad(D)\;1.512\qquad(E)\;3\)

I guess i can just plug it into the calculator using solve function,
but can you please show me how to solve this problem?
When i plugged into my TI, the answer i got was (A). . Right!

We can do some algebra first, but your calculator will be needed at the very end anyway . . .


\(\displaystyle \text{We have: }\;(\tan x - 1)^2 \;=\;4\)

\(\displaystyle \text{Take square roots: }\;\tan x - 1 \;=\;\pm2\)

\(\displaystyle \text{Then: }\; \tan x \;=\;1 \pm 2 \;=\;3,-1\)


\(\displaystyle \begin{array}{ccccc}\tan x \:=\:3 & \Rightarrow & x \:=\:\tan^{\text{-}1}(3) &\approx& 1.249,\:4.391,\:\hdots \\ \tan x \:=\:\text{-}1 & \Rightarrow & x \:=\:\text{-}\tfrac{\pi}{4} &\approx&\boxed{\text{-}\:\!0.785}\;3.927,\:\hdots \end{array}\)