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That is the definition. If you take your unit circle (a circle with radius 1 centered at the origin (0,0). you start at (1,0) and go counterclockwise around the circle 90° you end up at (0,1) that 0 is the cosine of the angle 90°

In fact, you don't even need the unit circle. Take a circle of any radius r, and draw a ray at 90 degrees. This will intersect the y-axis. So as above, the coordinates are (0,r) (instead of (0,1)) so cos(90 degrees)=x/r=0/r=0

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Q: Why is the cosine of 90 equal to 0?
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Related questions

What is the cosine of -90?

Cosine of -90 is 0.


How is cos 90 equal to 0?

The Unit Circle is a circle that has a radius of 1 and a center at the origin. If you look at the unit circle 90 degrees is at the point (0,1). Cosine is equal to the x value of a point on the Unit Circle. The line created to the point (0,1) on the unit circle when the degree is 90 is completely vertical, which in turn makes the x value 0 and thus, cosine of 90 = 0. Read more >> Options >> http://www.answers.com?initiator=FFANS


What is the cosine of 90 degrees?

The cosine of 90 degrees is zero.


What is cosine 0?

Cosine (0) = 1 Sin(0) = 0 The sine and cosine curves are two intertwining curves, that complement each other, hence the words 'Sine (Curve) and Cosine ( COmplementary Curve).


Law of cosines with a right angle?

The law of cosines with a right angle is just the pythagorean theorem. The cosine of 90 degrees is 0. That is why the hypotenuse squared is equal to the sum of both of the legs squared


What is the graphic representation of cosine function?

Just like the sine function displaced by pi/2. In other words the cosine equals 1 at 0 degrees, 0 at 90 degrees, -1 at 180 and so on.


What is the cosine of a ratio that has 0 as its numerator?

If the numerator is 0 AND the denominator is not 0, then the ratio is 0. And cosine of 0 is 1.


What is cos 90?

Cosine of 90 degrees is zero.


What is the formula for the y-intercept of a cosine function?

The Y-Intercept of the cosine function is X = 0, Y = cosine(0) = 1.


What is the value cosine 90?

Zero


Why is it tangent 90 degrees is undefined?

Because it tends to infinity. Additionally, tangent can be expressed as sin theta divided by cos theta. The sine of 90 is 1. The cosine of 90 is 0. That would be 1 divided by 0, or division by zero; which is undefined.


Why is it cosine 90 degrees is 0?

It helps to think as the sine and cosine as coordinates of a unit circle - a circle of radius 1, with center at the origin of the coordinates, i.e., point (0, 0). In this case, as you go around on the circle (starting at the right, coordinates (1, 0), and going counterclockwise), the cosine of the angle is simply the x-coordinate, and the sine of the angle is simply the y-coordinate. At 90°, the x-coordinate is 0, therefore the cosine is 0. Also, at 90° the y-coordinate is 1, therefore the sine is 1 (that's the maximum value it can have).