For an angle of 90 or 270 degrees. In radians, pi / 2 and 3 x pi / 2.
Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
The cosine of 90 degrees is zero.
It is 1.
The tangent of 90 degrees is undefined. This is because the tangent function is defined as the ratio of the sine to the cosine, and at 90 degrees, the cosine is zero, leading to division by zero. Therefore, the tangent approaches infinity as the angle approaches 90 degrees.
Zero
A "zero of a function" is a point where the dependent value (usually, Y) is zero. In the function f(x) = x2 - 2, for example, there are zeroes at -1.414 and +1.414.The zeroes of the sine function are at all integer multiples of pi, i.e. 0, pi, 2pi, 3pi, etc. The zeroes of the cosine function are at the same points plus pi/2, i.e. pi/2, 3pi/2, 5pi/2, etc.Another way to look at this is that the zeroes of sine are the even multiples of pi/2, and the zeros of cosine are the odd multiples of pi/2.
Cosine of 90 degrees is zero.
The domain of a function is the set of values of the independent variable for which the function is valid. In practice, this is the allowable values of X or, in this case, theta. The sine and cosine functions have a domain of all numbers from negative infinity to positive infinity. The tangent function, however, is sine(theta) / cosine(theta). Cosine(theta) has value of zero at theta equal to pi / 2, 3pi/2, 5pi/2, ... in the positive direction, and -pi/2, -3pi/2, -5pi/2, ... As a result, tangent(theta) is undefined at these values, so the domain of tangent is all numbers from negative infinity to positive infinity except all numbers n pi/2 where n is odd.
Yes, except at odd multiples of pi/2 radians, where the cosine is zero so that the division is not defined.
A function that depends on the value of an angle. One way to define it is with a unit circle (a circle with center in the coordinate origin, and radius of 1). To the right is zero, from there, a positive angle is counterclockwise. In this case, the sine is simply the y-coordinate, and the cosine is the x-coordinate of the point on the circle where the ray of the angle crosses the circle. The value of the sine (and cosine) obviously depends on the angle - that's why it is considered a "function". Sine, cosine, tangent, cotangent, cosecans, and secans can also be defined via right triangles; for more details see here: http://en.wikipedia.org/wiki/Sine#Sine.2C_cosine_and_tangent
Although it's not clear which distribution you're referring to, I sense that I know what you mean. This is one of those situations where a function is only asymptotically zero, which is to say that it reaches zero only in the limit. But, no matter how large the exponent is, it never actually reaches zero; therefore, the probability never becomes zero. It only becomes extremely small.
The tangent function, often denoted as tan(x), is a mathematical function defined in trigonometry as the ratio of the sine and cosine functions: tan(x) = sin(x) / cos(x). It represents the slope of a line that intersects the unit circle at an angle x and is periodic with a period of π. The tangent function is undefined at angles where the cosine is zero, such as π/2 and 3π/2, resulting in vertical asymptotes on its graph. It is commonly used in various applications, including physics, engineering, and geometry.