Question

find tan theta if sin theta= -2/3 and falls in quadrant 4. WILL GIVE A MEDAL TO WHO CAN HELP ME THE MOST.

Answer 1

Ok there a couple of ways you can do this. I'll go ahead with the easier way.

Consider a right angled triangle.

You should know sin theta=perpendicular/hypotenuse
and tan theta=perpendicular/base..

So as you have the value of sin theta, which gives you the values of perpendicular and hypotensue, you can find the base using Pythagoras theorem.

so you can find the value of tan theta..

Answer 2

You dont have to find that..

ok look.. as sin theta=-2/3, you can consider that perpendicular must be 2 units and hypotenuse must be 3 units.. as sn theta=perp/hyp.

yeah?

Answer 3

@yrelhan4 THANK YOU i appreciate it

Answer 4

You got the answer?
Also note as the question specifies that the angle is in the 4th quadrant, tan theta in the 4th quad is negative.

Answer 5

okay... but i thought the 4th quadrant was positive?

Answer 6

You need to memorise one line for this..
Add Sugar To Coffee..
What this means is..
A-All is positive in first quadrant..
S-Sin is poisitve in second quad
T-Tan is positive in 3rd quad
C-Cos in positive in 4th quad..

Answer 7

and the answer is \[-\frac{ \sqrt{5} }{ 3 }?\]

Answer 8

Yup. Well done.

Answer 9

thanks