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Why is the sine and cosine of a number no less than -1 and no greater than 1?
Wiki User
∙ 15y ago
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.
Wiki User
∙ 15y ago
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What trigonometric ratios cannot be greater than one?
Sine and cosine.
Why are the sine and the cosine of an acute angle always 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 .
If two integers have the same sign what is the sine of their sum?
Sine(A+ B) = Sine(A)*Cosine(B) + Cosine(A)*Sine(B).
What are the Differentiate the sine wave and cosine wave?
The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
How does the tangent function relate to sine and cosine?
Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
What trigonometric ratios cannot be greater than one?
Sine and cosine.
Why can tangent values be greater than 1 but sine and cosine values cannot be greater than 1?
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.
Why is the sine and cosine of a number no less than 1 and no greater than 1?
lol! it can be less than 1 too, upto -1! it cannot be greater than 1 because hypotenuse is always longer than the adjacent and opposite side... (from pythagoras theorem)
Why are the sine and the cosine of an acute angle always 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 .
If two integers have the same sign what is the sine of their sum?
Sine(A+ B) = Sine(A)*Cosine(B) + Cosine(A)*Sine(B).
How do you find the cosine and the sine?
Sine= Opposite/ Hypotenuse Cosine= Adjacent/ Hypotenuse
What are the Differentiate the sine wave and cosine wave?
The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
How does the tangent function relate to sine and cosine?
Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
Why are sine and cosine functions used to describe periodic?
because sine & cosine functions are periodic.
Which trigonometric functions always have values less than 1?
The sine and the cosine are always less than one.
How do you find sine cosine and tangent of 210 degrees?
Sine = -0.5 Cosine = -0.866 Tangent = 0.577
Do the equations sine plus cosine and sine squared plus cosine squared both equal 1?
No, they do not.
