What is the value of \tan \theta=\frac{1}{-1}?

Francisca Rodden

Francisca Rodden

Answered question

2022-01-15

What is the value of tanθ=11?

Answer & Explanation

Laura Worden

Laura Worden

Beginner2022-01-16Added 45 answers

Let z=−1+i=x+yi, with x=−1 and y=1.
Clearly z is in the second quadrant, since x<0 and y>0.
The polar form is z=r(cosθ+isinθ)
As you noted, r=2
Therefore, cosθ=12  and  sinθ=12,
so we can take θ=3π4
Note that π2<θ<π,  so  θ is indeed in the second quadrant.

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