What is the relationship between Trigonometry and Calculus?

Question

Broadly speaking.

Answer 1

They're significantly related through De Moivre's formula, which is:

(Cos(x) + i Sin(x))^n = Cos(nx) + i Sin(nx)

and Euler's formula, which is:

e^(i x) = Cos(x) + i Sin(x)

Both were originally derived through analysis of infinite series of trignometric functions, the infinite series in turn derived through calculus. A host of new properties of trigonmetric functions came to light with calculus, such as the differential of Sin(x) is Cos(x), and (almost) vice-versa:

d/dx (Sin(x)) = Cos(x)
d/dx (Cos(x)) = - Sin(x)

Calculus provided the bridge between trigonmetry as used in classical axiomatic geometry and trigonmetric functions invovled in curves in coordinate space. Trigonometric functions appear frequently in solutions of differential and integral equations in calculus, often in a abstract context that has no bearing on geometry.

Answer 2

Trig is the study of angles and deals mainly with sine, cosine, tangent, cosecant, secant and cotangent. Calculus is a whole different math topic that involves intergrals, derivatives and limits. In calculus, you use the trig functions but not in the same way as you do in trig. I am almost positive that you cant use calculus in trig.

Answer 3

Broadly speaking,I could have done without both in high school.

Answer 4

Many aspects of calculus can be demonstrated using trigonometric functions as sine, cosine, tangent, et cetera.

Answer 5

The last time I heard they were still causally dating.

Answer 6

numbers

Answer 7

srry i don't speek math and im not a nerd so i don't know

Answer 8

headaches and stress.