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
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).
The Y-Intercept of the cosine function is X = 0, Y = cosine(0) = 1.
sin(30) = sin(90 - 60) = sin(90)*cos(60) - cos(90)*sin(60) = 1*cos(60) - 0*sin(60) = cos(60).
It is 1.
The sine graph and the cosine graph are identical in shape, with the cosine graph shifted to the left by pi / 2, i.e. the sine starts at (x=0,y=0) and proceeds up with an initial slope of one, and the cosine starts at (x=0,y=1), and proceeds down with an initial slope of zero.
Cosine of -90 is 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
The cosine of 90 degrees is zero.
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).
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
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.
If the numerator is 0 AND the denominator is not 0, then the ratio is 0. And cosine of 0 is 1.
Cosine of 90 degrees is zero.
The Y-Intercept of the cosine function is X = 0, Y = cosine(0) = 1.
Zero
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.
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).