Trigonometry|Please help!

Question

Solve 2sin x = -1 over [0, 2pi]

Anyone that is able to guide me through the steps of this problem would be much appreciated!

Answer 1

2sinx = -1, divide by 2

sinx = -1/2

x = arcsin(-1/2) = an angle in quadrant 3 or 4 where sines are negative

= 210 or 330 degrees = 7pi/6 or 11pi/6 radians

Answer 2

Answer 3

there is a couple of pre requisites to solve this problem

1) knowing the Nature of the sign of the trigonometric functions

2) General solutions

having a solid understanding in these two will make this problem way to easy

Answer 4

Solve 2sin x = -1 over [0, 2pi] Dividing both sides by 2 we get

sin x = -1/2 The reference angle for this is π/6

sin is negative is quadrants 3 and 4 so the answers would be

x=7π/6, 11π/6

Answer 5

The first step is to isolate the sine function. Then solve this for the reference angle. After that use the properties of sine and find all other solutions within that interval. Let me show for a different example problem so that you can try this.

Example: 2 cos x = 1

Step 1. Divide by 2: cos x = 1/2

Step 2. Find reference angle by taking inverse cosine. x = cos^-1 (1/2) = π/3

Step 3. Cosine is positive in Quadrants I and IV. So the angles would be π/3 and 2π-π/3 = 5π/3.

Can you now try yours? Also, you can always set up a short session with me anytime.