If tan theta = 2/3 then sin theta= ?

A) +- 0.55

C) 0.55

Why is the answer A, I am sure the solution is simple, and can you please not use CAST as an explanation.

Thank you.

A) +- 0.55

C) 0.55

Why is the answer A, I am sure the solution is simple, and can you please not use CAST as an explanation.

Thank you.

How am I to explain it if I do not use the range in which tan is positive?

So - tan is positive between 0 and 90 - in this range sin is also positive

Also - tan is positive between 180 and 270 - in this range sin is negative


Given this - sin could be either positive or negative

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Use the identity cot^2 + 1 = cosec^2

to find sin you will up having to take a square root that leads to +-

Draw a right angled triangle, note that tan theta= opposite/adjacent. Use pythag to find the hypotenuse

I have tried this method, but only get the identities proving other identities or cancelling eachother out

I'm not really too sure what you mean.

Cot^2 x + 1 = cosec^2 x

since tan = 2/3 cot = 3/2

so (3/2)^2+1 = 1/sin^2
13/4 = 1/ sin^2
4/13 = sin^2 x

Now this leads to 2 roots. If you aren't sure what I mean, do the substituion y = sin x

so 4/13 = y^2
This has 2 roots, one negative, one positive.