Question

Give all trigonometric equation of Sinx and Cosx in their respective domains​

Answer 1

Step-by-step explanation:

The domain of the sine and cosine functions is all real numbers. The sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle. An angle's reference angle is the size angle, t, formed by the terminal side of the angle t and the horizontal axis.

Answer 2

Answer:

Trigonometric Functions

Significance

Trig functions are invaluable for applications and provide important examples. They link Calculus to Geometry. In Calculus, all trigonometric functions are functions of radians

Standard Notation

The functions sin(x) and cos(x) are defined by the picture on the right.

The other trigonometric functions are defined by

tan(x) = sin(x)/cos(x)

cot(x) = cos(x)/sin(x)

sec(x) = 1/cos(x)

csc(x) = 1/sin(x)

When expressing positive integer powers of trig functions, we write the exponent directly after the name of the function. Thus cos2(x) means [cos(x)]2. The notation cos-1(x) is reserved for the inverse cosine which is also called "arccosine" and can be written as arccos(x) or, on many calculators, acos(x). The same applies to inverse sine, inverse tangent, and so on.

Identities

From the Pythagorean relation on the right triangle OPQ, it is clear that

cos2(x) + sin2(x) = 1.

This important relation is called an identity. Identities are equations which are true for all values of the variable. Some other useful identities are

sin(x + y) = sin(x) cos(y) + sin(y) cos(x)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

sin(2x) = 2 sin(x) cos(x)

cos(2x) = cos2x - sin2x

1 + tan2(x) = sec2(x)

1 + cot2(x) = csc2(x)

AND THERE ARE LOTS MORE which we will not list here.