Trigonometry involves three ratios - sine, cosine and tangent which are abbreviated to \(\sin\), \(\cos\) and \(\tan\). The three ratios are calculated by calculating the ratio of two sides of a Answer link. dy/dx = sinx (3cos^2x- 1) y = (1 - cos^2x)cosx = cosx - cos^3x We know the derivative of cosx is -sinx. Letting y = u^3 and u = cosx, we have: (cos^3x)' = -sinx3u^2 = -sinx3 (cosx)^2 =-3cos^2xsinx The derivative of the entire expression is: dy/dx = -sinx - ( -3cos^2xsinx) dy/dx = 3cos^2xsinx - sinx dy/dx= sinx (3cos^2x- 1 Sine wave as a function of both space and time. The displacement of an undamped spring-mass system oscillating around the equilibrium over time is a sine wave. Sine waves that exist in both space and time also have: a spatial variable. x {\displaystyle x} that represents the position on the dimension on which the wave propagates. Answer link. Depending on the route you take, valid results include: sin^2 (x)/2+C -cos^2 (x)/2+C -1/4cos (2x)+C There are a variety of methods we can take: Substitution with sine: Let u=sin (x). This implies that du=cos (x)dx. Thus: intunderbrace (sin (x))_uoverbrace (cos (x)dx)^ (du)=intudu=u^2/2+C=color (blue) (sin^2 (x)/2+C Substitution sin(x) = 1. sin(x) − cos(x) = 0. sin(x) + 2 = 3. tan(x)2 = 4. Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. 7BCW.

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