Question

find the value of theta lying between 0 and 360 when tan theta=-1​

Answer 1

SOLUTION

TO DETERMINE

The value of θ lying between 0° and 360° when

tan θ = - 1

EVALUATION

Here it is given that

tan θ = - 1

Since tan θ is negative

So θ lies in 2nd or 4 th quadrant

When θ lies in 2nd quadrant

tan θ = - 1

⇒ tan θ = - tan 45°

⇒ tan θ = tan ( 180° - 45° )

⇒ tan θ = tan 135°

⇒ θ = 135°

When θ lies in 4 th quadrant

tan θ = - 1

⇒ tan θ = - tan 45°

⇒ tan θ = tan ( 360° 45° )

⇒ tan θ = tan 315°

⇒ θ = 315°

FINAL ANSWER

θ = 135° , 315°

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