Which of the following is a solution to the equation [tex]4 \sin(x) - 2 = -4[/tex]?

A. 0 degrees and 180 degrees
B. 270 degrees
C. 210 degrees and 330 degrees
D. 30 degrees and 150 degrees

Question

High School

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Answer :

KarpaT KarpaT · Answer 1 · 2025-04-07T20:59:47-04:00

The solutions to the equation 4 sin (x) - 2 = -4 are 210 degrees and 330 degrees. The correct option is: 210 degrees and 330 degrees.

Let's solve the equation step by step:

4 sin(x) - 2 = -4

Step 1: Add 2 to both sides to isolate the term with sin(x):

4 sin(x) = -2

Step 2: Divide both sides by 4:

sin(x) = -2/4

sin(x) = -1/2

Now, we need to find the angles whose sine is equal to -1/2. Remember that the sine function is negative in the third and fourth quadrants.

In the third quadrant (180 to 270 degrees), the sine is negative. The angle with sin(x) = -1/2 in the third quadrant is 210 degrees.

In the fourth quadrant (270 to 360 degrees), the sine is also negative. The angle with sin(x) = -1/2 in the fourth quadrant is 330 degrees.

So, the solutions to the equation are 210 degrees and 330 degrees. The correct option is: 210 degrees and 330 degrees.

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