Transcript Ex 12.2, 11 Find the derivative of the following functions: (i) sin x cos x Let f (x) = sin x cos x. Let u = sin x & v = cos x ∴ f (x) = uv So, f' (x) = (uv)' = u'v + v'u Here, u = sin x So, u' = cos x (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑠𝑖𝑛⁡〖𝑥=𝑐𝑜𝑠⁡𝑥 〗) & v = cos x So, v Thecotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x . The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x . What is cosine equal to? The cosine is equal to the adjacent side divided by the hypotenuse
\begingroup$ @Adrian yes but there is is a nice counterexample, $\sin(x)+\cos(x)=\frac{1}{2}\cos(x)$. In this case dividing by $\cos(x)$ is perfectly fine, since the if $\cos(x)=0$ would imply that $\sin(x)=0$, which is impossible.This is quite often used in school problems. $\endgroup$ -
limx→a f (x) g(x) = lim x→a f '(x) g'(x) So we have: lim x→0 x sinx = lim x→0 1 cosx = 1 cos0 = 1 1 = 1. NOTE. The question was posted in "Determining Limits Algebraically" , so the use of L'Hôpital's rule is NOT a suitable method to solve the problem. Therefore this solution is invalid. ANSWER TO THE NOTE. This limit can not be
Arcsineis an inverse of the sine function. In other words, it helps to find the angle of a triangle that has a known value of sine: arcsin(x) = y iff x = sin(y) As sine's codomain for real numbers is [−1, 1] , we can only calculate arcsine for numbers in that interval. This means that the domain of arcsin (for real results) is -1 ≤ x ≤ 1
Misc16 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers
Calculus Evaluate the Limit limit as x approaches infinity of (cos (x))/x. lim x→∞ cos (x) x lim x → ∞ cos ( x) x. Since −1 x ≤ cos(x) x ≤ 1 x - 1 x ≤ cos ( x) x ≤ 1 x and lim x→∞ −1 x = lim x→∞ 1 x = 0 lim x → ∞ - 1 x = lim x → ∞ 1 x = 0, apply the squeeze theorem. 0 0. Free math problem solver answers your
Cos45° Value. The exact value of cos 45 degrees is 1/√2 (in surd form), which is also equal to sin 45 degrees. It is an irrational number, equal to 0.7071067812 in decimal form. The approximate value of cos 45 is equal to 0.7071. Cos 45° = 1/√2 = √2/2. q3F1i.
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    • what is cos x divided by sin x