\(\displaystyle{\tan{{\left({x}\right)}}}={3}\). Find the value of \(\displaystyle{\sin{{\left({x}\right)}}}\)

Sanai Huerta

Sanai Huerta

Answered question

2022-03-30

tan(x)=3. Find the value of sin(x)

Answer & Explanation

Ishaan Stout

Ishaan Stout

Beginner2022-03-31Added 14 answers

If tan(x)=3, then tan2(x)=9.
This means that sin2x1sin2x=9. So, sin2(x)=910; in other words (at least if we're on the first quadrant), sin(x)=310
Demetrius Kaufman

Demetrius Kaufman

Beginner2022-04-01Added 10 answers

In general, if tan(x)=a then a2=tan2(x)=sin2(x)cos2(x)=sin2(x)1sin2(x) so
1a2=1sin2(x)sin2(x)=1sin2(x)1 so 1sin2(x)=1a2+1=1+a2a2 so sin2(x)=a21+a2 or sin(x)=a1+a2
Similarly, a2=tan2(x)=sin2(x)cos2(x)=1cos2(x)cos2(x)=1cos2(x)1 so 1cos2(x)=1+a2 so cos(x)=11+a2.
Now, try this for hyperbolic functions.

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