It will show that the two points have coordinates (x, y) and (x, -y). Because the cosine is the x-coordinate of the points on the unit circle, we can see the two points have the same cosine and opposite sine. The cosine is an even function; therefore, we can safely state that cos(-x) = cos x. 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 2 cos ix = ex +e−x 2 cos i x = e x + e − x. ie. cos ix = cosh(x) cos i x = cosh ( x) similarly subtracting the two equation gives. i sin ix = − sinh(x) i sin i x = − sinh ( x) in your question use. cos(a + b) = cos a cos b − sin a sin b cos ( a + b) = cos a cos b − sin a sin b. further substitute above transformations. Share. In trigonometry, reciprocal identities are sometimes called inverse identities. Reciprocal identities are inverse sine, cosine, and tangent functions written as “arc” prefixes such as arcsine, arccosine, and arctan. For instance, functions like sin^-1 (x) and cos^-1 (x) are inverse identities. Either notation is correct and acceptable. Expand the Trigonometric Expression cos(pi/2-x) Step 1. Apply the difference of angles identity. Step 2. Simplify terms. Tap for more steps Step 2.1. Simplify each e1.1i = cos 1.1 + i sin 1.1. e1.1i = 0.45 + 0.89 i (to 2 decimals) Note: we are using radians, not degrees. The answer is a combination of a Real and an Imaginary Number, which together is called a Complex Number. We can plot such a number on the complex plane (the real numbers go left-right, and the imaginary numbers go up-down): Transformation of cosx into sinx:By using complementary angles identities,cos ( x) = sin π 2 - x∴ sin ( x) + cos ( x) = sin ( x) + sin π 2 - xBy using the trigonometric identity,∴ sin 2 x + cos 2 x = 1 ⇒ cos x = 1 - sin 2 x∴ sin ( x) + cos ( x) = sin ( x) + 1 - sin 2 xHence, sin ( x) + cos ( x) = sin ( x) + sin ( π 2 - x)sin ( x For cos pi, the angle pi lies on the negative x-axis. Thus, cos pi value = -1. Since the cosine function is a periodic function, we can represent cos pi as, cos pi = cos (pi + n × 2pi), n ∈ Z. ⇒ cos pi = cos 3pi = cos 5pi , and so on. Note: Since, cosine is an even function, the value of cos (-pi) = cos (pi). PWb505V.