If \sin{x}=t, \quad x\in(\frac{3\pi}{2},2\pi), what is \tan x? So, according to

Naomi Hopkins

Naomi Hopkins

Answered question

2022-04-22

If sin{x}=t,x(3π2,2π), what is tanx?
So, according to the interval in which x lies, the value of the sine is negative, and positive for the cosine. Using trig identity I get that
cos{x}=±1sin2{x}=±1t2
Knowing the signs of sine and cosine, I pick 1t2. Computing tanx I get
tan{x}=sin{x}cos{x}=sin{x}1sin2{x}=t1t2

Answer & Explanation

hoppledhsy

hoppledhsy

Beginner2022-04-23Added 13 answers

You correctly found that
tanx=t1t2
Observe that since x(3π2,2π),t=sinx<0. Hence, t=|t|. Thus,
tanx=t1t2=|t|1t2

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