Question

The principle solutions of equation tan θ = -1 are ______ 

Options

• `pi/4, (5pi)/4`

• `pi/4, (3pi)/4`

• `(3pi)/4, (7pi)/4`

• `(3pi)/4, (11pi)/4`

Answer 1

The principle solutions of equation tan θ = -1 are `underline((3pi)/4, (7pi)/4)`.

Explanation:

tan θ = -1

⇒ tan θ = `-tan(pi/4)`

⇒ tan θ =  `tan(pi - pi/4) = tan((3pi)/4)`

and tan θ = `tan(2pi - pi/4) = tan((7pi)/4)`

Since 0 < `(3pi)/4 < 2pi` and 0 < `(7pi)/4 < 2pi`,

`(3pi)/4 "and" (7pi)/4` are the principle solutions.