(-∞, -1 ] U [1, ∞) Domain of cotangent. Sentence: Set of all real numbers, except integer multiples of π (180*)

Trigonometric Functions

The Domain of the cotangent function is the set of what? It is the set of all real numbers, except odd integer multiples of π (180°).

In reference to the coordinate plane, tangent is y/x, and cotangent is x/y. The domains of both functions are restricted, because sometimes their ratios could have zeros in the denominator, but their ranges are infinite.

The restriction that is placed on the domain values of the cosine function is 0 ≤ x ≤ π (see Figure 2 ). This restricted function is called Cosine. Note the capital “C” in Cosine.

The cotangent has a period of π, and we don’t bother with the amplitude.

Analyzing the Graph of y = tan x and Its Variations. The period of the tangent function is π because the graph repeats itself on intervals of kπ where k is a constant. If we graph the tangent function on −π2 to π2 , we can see the behavior of the graph on one complete cycle. tan(−x)=sin(−x)cos(−x)Definition of tangent.

Explanation: By definition, csc(x)=1sin(x) . Therefore, its period is the same as the period of sin(x) , that is, 2π .

In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side. In a formula, it is abbreviated to just ‘csc’. They can be easily replaced with derivations of the more common three: sin, cos and tan. …

By the Sum Rule, the derivative of 1−sin(x) 1 – sin ( x ) with respect to x x is ddx[1]+ddx[−sin(x)] d d x [ 1 ] + d d x [ – sin ( x ) ] . Since 1 1 is constant with respect to x x , the derivative of 1 1 with respect to x x is 0 0 .

The notation sin-1(x) has been misunderstood to mean 1/sin(x). So sin-1(x) means the inverse sine of x, that is, the function that undoes the sine function. It is not equal to 1/sin(x).

We know∫sinx=−cosx, hence ∫sinx2=−cosx2ddx(x2)=−cosx212. ⟹−2cosx2+2sinx2+C (where C is the integration constant). Therefore∫√1 – sinxdx = 2√1−sinx+C. Hence Option B is the correct answer.

The cosine double angle formula tells us that cos(2θ) is always equal to cos²θ-sin²θ. For example, cos(60) is equal to cos²(30)-sin²(30). We can use this identity to rewrite expressions or solve problems.