Question

tan (2theta + 8) = -0.489

theta = ?

i'm on my last attempt to solve this problem on my hw. I tried subtracting 8 from -0.489 then trying to find the inverse but no luck.... I got -4.245 as one of my answers,-0.7267, no luck so far :(

Answer 1

treat (2Ø+8) as you angle
then, do tan^-1 (.489) = x
x = .45481 radians
but the tangent was negative
so 2Ø+8 = π-.45481
2Ø = -5.313216..
Ø = -2.65661
or
2Ø+8 = 2π-.45481
Ø =-1.0858..

as you can see those two answers are negative, but you probably want answers from 0 --- 2π
we know the period of tan(2Ø+8) = 2π/2 = π
so by adding multiples of π we can get as many solutions as we want
other answers
-2.65661 + π = .48498
.48498.. + π = 3.626577..
3.626577 + π = 6.768.. , beyond 2π

-1.0858+π = 2.05578
2.05578+π = 5.19737

so in the domain 0 ≤ Ø ≤ 2π
Ø = .48498 , 2.05578 , 3.626577, and 5.19737

I checked all 4 answers, they work