How do you find the limit of x/sinx as x approaches 0? - Socratic
2016年3月3日 · lim x→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 ...
Differentiating sin(x) from First Principles - Calculus - Socratic
Graphical Relationship Between sin (x), x, and tan (x), using Radian Measure. Derivatives of y=sec (x), y=cot (x), y= csc (x) Differentiating Inverse Trigonometric Functions. Next. The derivative of \sin (x) can be found from first principles. Doing this requires using the angle sum formula for sin, as well as trigonometric limits.
How do you find an expression for sin(x) in terms of e^(ix
2018年6月4日 · The relation between the two sets of functions is an important one. Answer link. sinx = (e^ (ix) - e^ (-ix))/ (2i) Start from the MacLaurin series of the exponential function: e^x = sum_ (n=0)^oo x^n/ (n!) so: e^ (ix) = sum_ (n=0)^oo (ix)^n/ (n!) = sum_ (n=0)^oo i^nx^n/ (n!) Separate now the terms for n even and n odd, and let n=2k in the first ...
Fundamental Identities - Trigonometry - Socratic
Here are a few examples I have prepared: a) Simplify: tanx/cscx xx secx. Apply the quotient identity tantheta = sintheta/costheta and the reciprocal identities csctheta = 1/sintheta and sectheta = 1/costheta. = (sinx/cosx)/ (1/sinx) xx 1/cosx. =sinx/cosx xx …
What is sin(x) times sin(x)? + Example - Socratic
2015年4月16日 · sin(x)xxsin(x) = sin^2(x) There are other answers, for example, since sin^2(x)+cos^2(x) = 1 you could write sin(x)xxsin(x) = 1-cos^2(x) (but that's not much of a simplification)
What does cosx sinx equal? - Socratic
2016年3月7日 · Answer link. cos (x)sin (x) = sin (2x)/2 So we have cos (x)sin (x) If we multiply it by two we have 2cos (x)sin (x) Which we can say it's a sum cos (x)sin (x)+sin (x)cos (x) Which is the double angle formula of the sine cos (x)sin (x)+sin (x)cos (x)=sin (2x) But since we multiplied by 2 early on to get to that, we need to divide by two to make ...
What is #sin(x-90)#? - Socratic
2015年12月17日 · If sinA=4/5 and cosB= -5/13, where A belongs to QI and B belongs to QIII, then find sin(A+B).... See all questions in Sum and Difference Identities Impact of this question
Proving Identities - Trigonometry - Socratic
The Trigonometric Identities are equations that are true for Right Angled Triangles. Periodicity of trig functions. Sine, cosine, secant, and cosecant have period 2π while tangent and cotangent have period π. Identities for negative angles. Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions.
How do you simplify #sin(arccos(x))#? - Socratic
2016年10月21日 · sin(arccos(x)) = sqrt(1-x^2) From Pythagoras, we have: sin^2 theta + cos^2 theta = 1 If x in [-1, 1] and ...
What is sin (x)+cos (x) in terms of sine? - Socratic
2015年4月15日 · The coefficients of sinx and of cosx must be equal so. Squaring and adding, we get. R2cos2α +R2sin2α = 2 so R2(cos2α +sin2α) = 2. R = √2. And now. so α = cos−1(1 √2) = π 4. sinx + cosx = √2sin(x + π 4) Please see two possibilities below and another in a separate answer. Using Pythagorean Identity sin^2x+cos^2x=1, so cos^2x = 1 ...