Explained Visually. Sine and cosine — a.k.a., sin (θ) and cos (θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin (θ) is the ratio of the opposite side to the hypotenuse, while cos (θ) is the ratio of the adjacent side to the hypotenuse. No matter the size of the triangle, the values

Find the value for θ θ by substituting the coefficients from sin(x) sin ( x) and cos(x) cos ( x) into θ = tan−1(b a) θ = tan -1 ( b a). Divide 1 1 by 1 1. Linear combinations of trigonometric functions dictate that asin(x)+bcos(x) = ksin(x+θ) a sin ( x) + b cos ( x) = k sin ( x + θ). Substitute the values of k k and θ θ.
0. The statement: eix = sin(x) + i cos(x) e i x = sin ( x) + i cos ( x) is derived using Taylor series which can be proven like so. Just sum cos(x) cos ( x) and sin(x) sin ( x) for f(x) f ( x) to convince yourself. If you sum up those two Taylor series, it will give you the Taylor series for eix e i x.
cos x = AC (1) We take this same triangle and rotate it by 90°. Call this triangle ΔA′B′C′. Again by the definition of sin. sin(90° + x) = y-coordinate of B. sin(90° + x) = A′C′ (2) Now, since this is the same triangle, just rotated, A′C′ = AC.
It flips the function sin (x), where the x axis is the mirror. Draw this as well. Notice that both reflections end up looking the same. That's why sin (-x) = -sin (x). Now let's do the same thing for the cosine function. Draw cos (x). And cos- (x) will flip it by the y-axis. And -cos (x) will flip it by the x-axis.
sin ( sin ( x)) ≈ 0.8801 sin ( x) + 0.0391 sin ( 3 x) + 0.0005 sin ( 5 x). (See the plot of the difference of the two functions here .) The numbers in the expression given are rounded to four decimal places and we could add more terms of the form sin ( ( 2 n + 1) x), but their coefficients will get smaller and smaller. v0Rqf6h.
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    • what is cos x sin