Now, there are 360° in a circle, how many times does 360° go into 1860°?
well, let's check that,
now, this is a negative angle, so it's going clockwise, like a clock moves, so it goes around the circle clockwise 5 times fully, and then it goes 1/6 extra.
well, we know 360° is in a circle, how many degrees in 1/6 of 360°? well, is just 360/6 or their product, and that's just 60°.
so -1860, is an angle that goes clockwise, negative, 5 times fully, then goes an extra 60° passed.
5 times fully will land you back at the 0 location, if you move further down 60° clockwise, that'll land you on the IV quadrant, with an angle of -60°.
therefore, the csc(-1860°) is the same as the angle of csc(-60°), which is the same as the csc(360° - 60°) or csc(300°).
well, let's check that,
now, this is a negative angle, so it's going clockwise, like a clock moves, so it goes around the circle clockwise 5 times fully, and then it goes 1/6 extra.
well, we know 360° is in a circle, how many degrees in 1/6 of 360°? well, is just 360/6 or their product, and that's just 60°.
so -1860, is an angle that goes clockwise, negative, 5 times fully, then goes an extra 60° passed.
5 times fully will land you back at the 0 location, if you move further down 60° clockwise, that'll land you on the IV quadrant, with an angle of -60°.
therefore, the csc(-1860°) is the same as the angle of csc(-60°), which is the same as the csc(360° - 60°) or csc(300°).