Solve the equation

Question

tan x = -4.5

a) on the interval (-π/2,π/2)

b) on the interval (-infinity,infinity)

c) on the interval [0, 2π).

Answer 1

a) x = -77.5 degrees rounded off to one decimal place

or x = -.43pi radians

b) x = 102.5 degrees + n180 where n = any integer

or 0.57pi radians + npi where n= any integer

or x=-77.5 degrees + n180 where n = any integer

or x=-0.43pi radians + npi where n= any integer

c) x = 102.5 degrees and 360-77.5 = 282.5 degrees

or x= 0.57pi or 1.57pi radians + npi where n= any integer

tangents are only negative in quadrant II or IV

put 4.5 into a calculator and push the inverse tangent function, it reads 77.47119229

it is negative in quadrant IV or -77.5

it's supplementary angle is also negative, in quadrant II. 180-77.5 = 102.5

convert degrees to radians by multiplying by pi/180. 77.5(pi/180) = 0.43pi radians

Answer 2

tanx = - 4.5; general solution x = - tan^-1(4.5) + πn = -1.3521 + πn.

a) n = 0, x = - 1.3521

b)x = - 1.3521 + πn, n = 0,±1, ±2, ...

c) n = 1 x = 1.7895 and n = 2, x = 4.9311