T/F: When sin is 1/2, then the degree MUST EQUAL 30?

Question

Is this true? Couldn't the angle be 150?

Answer 1

The answer is no, it isn't necessarily true, and the angle could be 150 degrees.

Sine is a repeating function there are an infinite number of values x which would yield the value 1/2 from the function y = sin x.

Because the sine function repeats, the inverse of the sine function is not itself a function, but it is common in mathmatics to, by limiting the range of the inverse, to make it a function.

So when using the inverse sin FUNCTION (y = Arcsin x), which has a range from negative 90 degrees to positive 90 degrees, inclusive, the only value in the range which will yield an answer of 1/2 is, indeed, 30 degrees.

hopefully that made sense.

Answer 2

Yep. 150 degrees will also work. And if you allow angles greater than 360 degrees, there are an infinite number of angles that will give 1/2.

If this came up in a certain context where a 150 degree angle wouldn't make sense, then 30 degrees would be your answer. It depends on things other than just the sine giving a value of 1/2.

Answer 3

If you limit
arcsin x = y where
-1 <= x <= 1

But if you don't, then the angle can be 150, 390, 510, -210, -330, etc.

Why limit the domain of x? If you do not, then the arcsin relation will not be a function. Having it as a function is always useful in some fields of mathematics like calculus.

^_^

Answer 4

sin 30 = 1/2
sin 150 = 1/2

I think sine is positive in the first and second quadrants

Answer 5

Sine of 30 stages = a million/2 Sine of a hundred and fifty stages = a million/2 Sine of 210 stages = -a million/2 Sine of 330 stages = -a million/2 Your answer -30 stages (it quite is measured clockwise) is right because it corresponds to 330 (stages measured anti-clockwise). thinking precise-hand precise quadrant as a beginning 1st quadrant 0 to ninety deg), and shifting anti-clockwise to the 2d quadrant (ninety to a hundred and eighty deg), and directly to third quadrant (a hundred and eighty to 270 deg) and ultimately the 4th quadrant (270 to 360 deg) to end a circle, the 1st quadrant, sine, cosine and tangent of an perspective in that 1st quadrant supplies +ve effect. interior the 2d quadrant, i.e. between ninety stages and a hundred and eighty stages, sine supplies +ve effect, tan and cos supply -ve effect, in third quadrant, i.e. between a hundred and eighty and 270 stages, tan of perspective in that third quadrant supplies +ve effect, sine and cos supply -ve effect, and ultimately interior the 4th quadrant, i.e. between 270 and 360 stages, cos supplies +ve effect, tan and sine supply -ve effect.

Answer 6

sin(150) = (1/2)

ANS : False

Answer 7

Yes and No

Answer 8

Very simply put, yes