Quadrant

Jan 2013
6
0
Uk
Can anyone answer the following 3 questions? And state quadrant?


(1) Sin 186


(2) tan 150


(3) cos(-65)
 
Dec 2011
2,314
916
St. Augustine, FL.
Let's look at the quadrants first...assuming the arguments are in degrees, can you state what range of degrees the 4 quadrants encompass, for \(\displaystyle 0^{\circ}\le\theta<360^{\circ}\)?
 
Jan 2013
6
0
Uk
I have an idea just wanted to see if I was correct without actually embarrassing myself. Can you answer the first question number 1?
 
Dec 2011
2,314
916
St. Augustine, FL.
Quadrant I: \(\displaystyle 0^{\circ}<\theta<90^{\circ}\)

Quadrant II: \(\displaystyle 90^{\circ}<\theta<180^{\circ}\)

Quadrant III: \(\displaystyle 180^{\circ}<\theta<270^{\circ}\)

Quadrant IV: \(\displaystyle 270^{\circ}<\theta<360^{\circ}\)

So, in which quadrant is \(\displaystyle 186^{\circ}\)? And don't worry about embarrassing yourself, there is no shame in asking questions, the only shame is in not asking when you don't know. (Nod)
 
Jan 2013
6
0
Uk
Lol ok cool I have no idea when it comes to sin 186... Or which quadrant it would be in.
 
Dec 2011
2,314
916
St. Augustine, FL.
Which range of values does 186° match? Is it in between 0° and 90°, or in between 90° and 180°, or in between 180° and 270°, or in between 270° and 360°?
 
Dec 2011
2,314
916
St. Augustine, FL.
Yes, since 180 < 186 < 270, we know 186° is a quadrant III angle. As such, what can we expect the sign of sin(186°) to be? Will it be negative or positive?