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In a right triangle, the sine of the angle is equal to the

(leg opposite the angle) divided by the (hypotenuse).

It's well known that the hypotenuse is always the longest side in the right triangle,

so this division can never come out to be more than ' 1 '.

Q: Why is the sine of an angle less than 1?

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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.

No angle has a sine function greater than 1.

1 it can not used when the angle more than 45 degrees.....

The sine and the cosine are always less than one.

Sine = Opposite divided by Hypotenuse Opposite is the side of the triangle opposite the angle (in this case the 90o angle). Hypotenuse is the side opposite the right angle in a right angle triangle. Therefore, Sine 90 = 1 because the opposite side and the hypotenuse are the same side, they are both opposite the right angle.

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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.

Well, the easiest way to go at it is simply to remember thatthe sine and cosine of any angle are always less than 1 .

no - nor less than minus 1.

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.

No angle has a sine function greater than 1.

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.

It is 1.

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

1 it can not used when the angle more than 45 degrees.....

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.

If you mean the sine function, it is dependent on an angle. For example, the sine of an angle of zero degrees is zero; the sine of an angle of 90 degrees is one; for an angle of 180 degrees, the sine is again 0; if you make a graph, you get a curve that looks like a wave. In general, the values the sine function can take are between 1 and -1, inclusive.

The sine and the cosine are always less than one.