bobsmith76 said:Homework Statement
I don't see how they're going from
sec x cot x to csc x
and
csc x tan x to sec x
You should not only recognize the trig identities, but different variations of them. For instance,bobsmith76 said:Homework Statement
I don't see how they're going from
sec x cot x to csc x
and
csc x tan x to sec x
The derivative of sec x is sec x tan x not csc x tan x
and the derivative of csc x is -csc x cot x
and if it's an identity then they didn't care to inform me of that at this website
http://www.sosmath.com/trig/Trig5/trig5/trig5.html
Trigonometric antiderivatives are functions that represent the inverse operations of trigonometric derivatives. They are used to find the original function that was differentiated to get a given trigonometric function.
To find the antiderivative of a trigonometric function, you must use the reverse chain rule and the basic antiderivative formulas for trigonometric functions. It involves using substitution, integration by parts, or other integration techniques.
The basic antiderivative formulas for trigonometric functions are:
- For sine: ∫ sin(x) dx = -cos(x) + C
- For cosine: ∫ cos(x) dx = sin(x) + C
- For tangent: ∫ tan(x) dx = -ln|cos(x)| + C
- For cotangent: ∫ cot(x) dx = ln|sin(x)| + C
Trigonometric antiderivatives are used in various real-world applications, such as in physics, engineering, and finance. They can be used to model and solve problems involving periodic motion, such as the motion of a pendulum or a spring. They are also used in calculating areas and volumes of curved shapes, and in determining the growth and decay of certain processes.
No, not all trigonometric functions have an antiderivative that can be expressed in terms of elementary functions. Some trigonometric functions, such as secant, cosecant, and their inverses, have more complex antiderivatives that cannot be written using basic formulas. These functions require advanced techniques, such as partial fractions or integration by parts, to find their antiderivatives.