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Sketch the angle with the given measure, and its reference triangle. Then find the required ratio?

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14. csc 225° =
15. cot -150° =
asked Oct 31, 2014 in TRIGONOMETRY by anonymous

2 Answers

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(14).

csc(225o)

The angle 225o lies in third quadrant and the reference angle is

θ' = 180o + 45o = 45o.

The cosecant is negative in Quadrant III, so

csc(225o) = (-) csc(45) = - (√2)/1.

We know that csc(θ) = r/y, therefore r = √2 and y = -1

Find the x-value by using formula: r2 = x2 + y2.

2 = x2 + (-1)2 ⇒ x = ± 1.

The point lies in the third quadrant x < 0 and y < 0.

Therefore, point (x, y) = (-1, -1).

Graph:

answered Nov 1, 2014 by casacop Expert
edited Nov 1, 2014 by casacop
0 votes

15).

cot(-150o)

Because - 150o + 360o = 210o, it follows that -150o is coterminal  with  the third-quadrant angle 210o. So the reference angle is

θ' = 210o - 180o = 30o.

The cotangent is positive in Quadrant III, so

cot(-150o) = (+) cot(30) = √3/1.

We know that csc(θ) = x/y, therefore x = √3 and y = 1.

Find the r-value by using formula: r = (x2 + y2).

r = (x2 + y2) = r = [(√3)2 + (1)2] = = 4 = 2.

The point lies in the third quadrant x < 0 and y < 0.

Therefore, point (x, y) = (-√3, -1).

Graph:

answered Nov 1, 2014 by casacop Expert
edited Nov 1, 2014 by casacop

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