Question

Find sin (theta/2), where tan theta= -3/4, theta in QIV

Answer 1

Use the Pythagorean Theorem to find the hypotenuse. Then use the definition of sin and remember that sin is negative in Q IV

Answer 2

I know that the hypotenuse is 5. And i know that the answer is sqrt 10/10 but i do not understand how to get that

Answer 3

The answer is -3/5

Answer 4

Oh no. Sorry. I just saw that you want the sin of theta/2

Answer 5

you have to use the half angle formula but I keep getting the wrong answer

Answer 6

\[\sin(\frac{\theta}{2})=\sqrt{\frac{1-\cos \theta}{2}}\]

Answer 7

=\[\sqrt{\frac{1-\frac{4}{5}}{2}}=\sqrt{\frac{\frac{1}{5}}{2}}=\sqrt{\frac{1}{10}}=\frac{\sqrt{10}}{10}\]

Answer 8

Make it negative because the sin is negative in Quadrant 4

Answer 9

oh my goodness, thank you so much! I was squaring the (4/5). I'm not sure why haha

Answer 10

yw

Answer 11

and that is what I also dont understand, my homework says that its positive

Answer 12

I guess it would be positive because if the angle is in the 4th quadrant, we would have:
\[270^{o}<\theta <360^^{o}\]

Answer 13

\[270<\theta <360\]

Answer 14

So
\[135<\frac{\theta}{2}<180\]

Answer 15

And those angles would be in quadrant 2 so the sin would be positive.

Answer 16

makes sense! thank you

Answer 17

yw