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Q: Is sine greater than one

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The sign is >. Sine is a trigonometric function.

Sine and cosine.

the sine of an angle can't be greater than 1.0

no - nor less than minus 1.

It's not. The sine of 32 degrees is approximately 0.53. The sine of 59 degrees is approximately 0.86. For a definition of sine, see: http://en.wikipedia.org/wiki/Trigonometric_function .

Sine and cosine cannot be greater than 1 because they are the Y and X values of a point on the unit circle. Tangent, on the other hand, is sine over cosine, so its domain is (-infinity,+infinity), with an asymptote occurring every odd pi/2.

If you look at the definition of the sine function in a triangle, you'll discover that the maximum possible value of the sine function is ' 1 ' and the minimum possible value is ' -1 '. There's no angle that can have a sine greater than ' 1 ' or less than ' -1 '. So the absolute value of the sine of anything is always ' 1 ' or less.

You can only find the inverse of sine for number less than or greater than 1. An improper fraction is not acceptable either because the ratio is opposite over hypotenuse. The hypotenuse will always be the longest, so there you go.

No. The sine of an acute angle is less than 1. An acute angle is less than 90 degrees. The sine of 0 degrees is 0, and the sine of 90 degrees is +1. So the sines of the angles between 0 degrees and 90 degrees are less than 1.

Since the hypotenuse (denominator) is always greater than the opposite or adjacent side (numerator), the ratio will always be smaller than one.

The sine of an angle x is defined as the ratio of the opposing side to the hypotenuse, in a right triangle having x as one of its acute angles. If it was greater than 1, it would mean the opposing side was longer than the hypotenuse. Try to draw a right triangle with one of the sides longer than the diagonal. You'll notice it's impossible. So the sine cannot be greater than 1. Fitting the triangle into a circle of radius 1, such that the angle x is located at the origin and the hypotenuse is a radius of the circle, you can define "sine of x" for any angle. Since the triangle may end up flipped in any direction, including the negative x and y axis, it turns out that the sine of any number is between -1 and +1. The cosine is simply the sine of the complementary angle (90 - x). So it must also be contained between -1 and +1.

The sine of an angle between 0 and 180 degrees is positive. The sine of an angle between 180 degrees and 360 degrees is negative. At 0, 180 and 360 degrees the sine is 0.The sine is a periodic function with period 360 degrees, so angles differing by a multitude of 360 degrees have the same sine. Hence, for instance, the sines of the angles 0, 360, 720, ... are equal, namely 0.In any right triangle the sine of one of the non-right angles will be positive, since these are greater than 0 and less than 90 degrees.

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