Mathematics 30 Online
OpenStudy (anonymous):

sinO(theta)=sqrt3/2 and tanO(theta)>zero; find cosO(theta)?

OpenStudy (anonymous):

Draw out a special triangle.. do you need the answer in radians or degrees?

OpenStudy (anonymous):

Doesn't say. I think it's in radians because of the sqrt of 3/2 thing

OpenStudy (anonymous):

sin(theta)=sqrt3/2 - theta= pi/3 in the first quadrant, 2pi/3 in the second quadrant tan(theta) > 0 - 0<theta< pi/2 and pi<theta< 3pi/2

OpenStudy (anonymous):

So is that cos(theta)?

OpenStudy (anonymous):

Is it telling you to get cos(theta) from the questions before it?

OpenStudy (anonymous):

Yeah, it just says find cos(theta) from the sin and tan information before it.

OpenStudy (anonymous):

Anywhere cos(theta) is positive or...?

OpenStudy (anonymous):

Yeah, I'd guess from it being positive.

OpenStudy (anonymous):

Ahs sorry I must've misinterpreted the question the first time I read it. So based on sin(theta)=sqrt3/2, tan(theta)>0, cos(theta) would have to be 1/2, if all the answers are supposed to be positive. If you need further explanations feel free to ask.

OpenStudy (anonymous):

I would love some further explanation, please! And thank you!

OpenStudy (anonymous):

Alright no problem :P.. Do you remember learning the CAST rule in school?

OpenStudy (anonymous):

Noo...Haha.

OpenStudy (anonymous):

These two rules will really help you in this unit, basically the CAST rule means in quadrant 1 anything( sin, cos, tan) from 0<(theta)< pi/2 will be positive, in quadrant 2 only sin pi/2<theta< pi will be positive and so on. On the right side these are the special triangles you should remember cause most of the questions are based off of them. The first one shows the special angles for pi/3 (60 degrees) and pi/6 (30 degrees). The second one is for pi/4 (45 degrees)

OpenStudy (anonymous):

Ohhh okay, I get it kind've. So how do you get cos off of those?

OpenStudy (anonymous):

This explains the first part of the sin thing. you notice how 2pi/3 will only be positive in the second quadrant if we were dealing with sin. However, the next part of the question says that tan(theta)>0, which eliminates the second possibility of the theta being 2pi/3

OpenStudy (anonymous):

OpenStudy (anonymous):

You seriously are the biggest lifesaver ever. Thank you so much!

OpenStudy (anonymous):

Hope my explanations weren't too confusing, glad I could help though :3!

OpenStudy (anonymous):

No I totally understood them! Thank you!!