Algebra Inputs Trigonometry Inputs Calculus Inputs Matrix Inputs sin(nπ) Differentiate w.r.t. n πcos(πn) Evaluate sin(πn)
There is another approach to rigorous infinitesimals in which it would be done the way Euler did it, saying that if $\theta$ is infinitely small then $\dfrac{\sin\theta}\theta = 1.$ It's called "smooth infinitesimal analysis". In that approach, the square of an infinitesimal is $0$, ...
cos(x + pi/6) - cos(x - pi/6) = 1. Find all solutions of the equation in the interval [0, 2 pi). sec theta + square root 2 = 0 Write your answer in radians in terms of pi. If there is more than one solution, separate th...
Thus we define the trigonometric functions by displaystyletantheta=t,quadcostheta=(1+t²)⁻¹/²,quadsintheta=t(1+t²)⁻¹/² where the point displaystyle(t,theta) is on the graph...
To find the sin of theta/2: Write down the sine half-angle equation: sin(θ/2) = ±√[(1-cos(θ))/2]. Replace theta θ within the equation and solve the square root. To choose the sign, follow this rule: The result is positive (+) if the half angle lies in the I or the...
, in particular of the square of the sum of sine and cosine of theta: ( sin ( θ ) + cos ( θ ) ) 2 = sin 2 ( θ ) + cos 2 ( θ ) + 2 sin ( θ ) cos ( θ ) ( sin ( θ ) + cos ( θ ) ) 2 = sin 2 ( θ ) + cos ...
Common trigonometric functions have periods that are multiples of π; for example, sine and cosine have period 2π, so for any angle θ and any integer k, displaystylesintheta=sinleft(theta+2pi kright)textandcostheta=cosleft(theta+2pi kright). Many of the appearances of π in the ...