please help, 2sin(x=-1 where 0_<x>_360?

Question

by the way this is on a non-calculator exam paper, srry for nt tellin you earlier

Answer 1

Non calculator? So, a solution requires that you solve the equation sin (theta) = -0,5. How, one would do that? We will solve sin (- theta) = 0,5, which is equivalent. Theta is the angle opposite to a side of length 0,5 in a rectangle triangle with hypotenuse of length 1, which is adjacent to the angle -theta. If you flip this rectangle triangle around the other side adjacent to the angle, the two triangles together creates an equilateral triangle with all three sides of length 1. The angles all have 60 degrees. So, our angle -theta is half of 60 degrees, which is 30 degrees. So theta = -30.

We use sin (theta) = sin(180 - theta ) to get sin(210) = -0,5. We use sin (theta ) = sin (theta + 360) to get sin(330) = -0,5.

Answer 2

First find what sin(x) = (.1/2) = -0.5

If you picture the sinusoid, it crosses the θ axis at 0, reaches 1 at 90º then stays positive until it crosses the axis again at 180º. Then it goes to -1 at 270º and stays negative for the rest of the cycle.

So, sin(x) = -0.5 can happen twice, once in the 3rd quadrant (180 - 270º) and once in the 4th quadrant (270º - 360º).

Now plug -.5 into your calculator and find the arcsin. (my calculator says -30º)

-30º is the same as 360 - 30 = 330º That's one of your solutions because x = 330 ≥ 360.

Back to the picture. The negative part of the sine wave is symmetric on both sides of 270º.

330 degrees is 60º more than 270º. So by symmetry the value of the sine wave at 270-60º should be the same as at 270º + 60º.

Sin (270-60) = sin (210) = sin (330) = -0.5

So x = 210º and 330º or equivalently, x = 270º±60º

Another way to look at it that gives the same answer is that because of symmetry, the sin at 360º - 30º is the same as the sin 180º + 30º. Those numbers give 210º and 330º too.

Answer 3

I will assume you mean

2sin(x) = - 1

sin(x) = -1/2
x = -30º ...

Sketching sin(x) shows sin(x) is negative where 180º < x < 360º

There will be another solution at 360º more than -30º since the function repeats itself.

-30º + 360º = 330º

This solution is 30º away from 360º so because the graph is symmetrical the other root must be 30º degrees more than 180º i.e. 210º

Therefore the solutions of

2sin(x) = - 1 where 0º < x < 360º

are at x=210º and x=330º.

Answer 4

sin x = - 1 / 2
inv sin (1/2) = 30°
Angle is in 3rd and 4th quadrants.
x = 210° , x = 330°

Answer 5

2sinx= -1
or,sinx= -1/2
or, sinx= sin(180+30) or sin(360-30)
or x= 210 or 330