(1) Sin 186

(2) tan 150

(3) cos(-65)

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 $0^{\circ}\le\theta<360^{\circ}$?

I have an idea just wanted to see if I was correct without actually embarrassing myself. Can you answer the first question number 1?

Quadrant I: $0^{\circ}<\theta<90^{\circ}$

Quadrant II: $90^{\circ}<\theta<180^{\circ}$

Quadrant III: $180^{\circ}<\theta<270^{\circ}$

Quadrant IV: $270^{\circ}<\theta<360^{\circ}$

So, in which quadrant is $186^{\circ}$? 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.

Lol ok cool I have no idea when it comes to sin 186... Or which quadrant it would be in.

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°?

Guessing 3rd quadrant 180 and 270

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?