How to solve for x

Question

x 0≤x<2pie

 

a) -tanx = √3                           b)solve to nearest tenth of a degree: 2sec theta+4=9

Answer 1

a) -tan x = √3

 

and tan x = -√3

Tan is negative in the 2nd and 4th quadrants.

 

Recalling the unit circle, tan x = √3 when sin x= √3/2 and cos x = 1/2.  This is the case when x = 60^o or π/3.

But we want -√3, which occurs at x = 2π/3 and 5π/3.

 

 

b) 2sec θ + 4 = 9

2 sec θ = 5 and

sec θ = 5/2

Since sec θ = 1/cos θ, we have 

cos θ = 2/5

This is not on the unit circle, so we have to resort to a calculator.

θ = cos^-1(2/5) = 66.4^o