This is a Trigonmetry question- Find all x on [0 degrees, 360 degrees) for which csc(x)=-2.?

Question

Okay, guys this is the answer to the question.

X=120 degrees, X=330 degrees

Some of you were right with this question, Thanks

Answer 1

If csc(x) = -2, that means that sin(x) = -1/2 because cosecant = 1/sine.

One angle whose sine is -1/2 is 330 degrees and the other is 210 degrees. These are the only angles between 0 and 360 whose cosecant is -2.

Answer 2

csc(x) = 1/sin(x)

So rephrase the questions as:

1/sin(x) = -2
or sin (x) = -1/2

Since sin (x) = opposite/hypotenuse (or y/r), -1/2 is applicable to any angles where y = -1 and r = 2. This specific right triangle has sides,
-1 , +sqaureroot(3) and 2 or
-1 , -sqaureroot(3) and 2.
and angles 30, 60 and 90.

Since y= -1, it is the shorter leg, and it extends down from the the positive or negative x-axis 30 degrees, representing angles:
360 - 30 or 330 degrees and
180 + 30 or 210 degrees.

Answer 3

csc(x) = -2
1/(sin(x)) = -2
sin(x) = (-1/2)
x = sin^-1(-1/2)
x = 210° or 330°

Once i used my calculator, it gave me -30°, which is the same as saying 330°, since that was 30° from 360°, i also worked 180° + 30°, which gives me 210°. Try it and you will get sin(210°) to be (-1/2)

Answer 4

csc x = -2

Use csc x = 1/sin x
1/sin x = -2

Multiply sin x to both sides
1 = -2 sin x

Use symmetric property
-2 sin x = 1

divide 2
-sin x = 1/2

Use - sin x = sin (-x)
sin (-x) = 1/2

therefore,
-x = arcsin 1/2
-x = 30, 150, -210, -330
x = -30, -150, 210, 330

Since 0 < x < 360 the final answer is
x = 210, 330

^_^

Answer 5

(2n*pi - pi/6) and (2n*pi + pi/6) where n is an integer
pi = 180 deg

Answer 6

check with drmath.org
TM