advanced functions

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1. calculus

   Find complete length of curve r=a sin^3(theta/3). I have gone thus- (theta written as t) r^2= a^2 sin^6 t/3 and (dr/dt)^2=a^2 sin^4(t/3)cos^2(t/3) s=Int Sqrt[a^2 sin^6 t/3+a^2 sin^4(t/3)cos^2(t/3)]dt =a Int

2. Calculus

   Find the exact values of x in the interval [0, 4π] that satisfy the equation sin x = -√2 / 2 (refer to y = sin x or y = cos x )

3. math

   1)In triangle ABC, C=60 degrees, a=12, and b=5. Find c. A)109.0 B)10.4 C)11.8 D)15.1 I chose B 2)Which triangle should be solved by beginning with the Law of Cosines? A)A=115 degrees, a=19, b=13 B)A=62 degrees, B=15 degrees, b=10

4. Trig

   The lengths QR, RP, and PQ in triangle PQR are often denoted p, q, and r, respectively. What do the formulas 1/2 pq sinR and 1/2 qr sin P mean? After you justify the equation 1/2 pq sinR = 1/2 qr sin P, simplify it to a familiar

1. Calculus 12th grade (double check my work please)

   1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y C.-2/3tan (2x/3y) D.-2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) with

2. Math

   Suppose f(x) = sin(pi*cosx) On any interval where the inverse function y = f –1(x) exists, the derivative of f –1(x) with respect to x is: a)-1/(cos(pi*cosx)), where x and y are related by the equation (satisfy the equation)

3. Trig

   4. Asked to simplify the expression sin(180−è), Rory volunteered the following solution: sin(180−è) = sin 180−sin è, and, because sin 180 is zero, it follows that sin(180−è) is the same as −sin è. Is this answer

4. Math

   The line has equation y=2x+c and a curve has equation y=8-2x-x^2. 1) for the case where the line is a tangent to the curve, find the value of the constant c. 2) For the case where c = 11, find the x-coordinates of the points of

1. Trig (math)

   1.) Write the complex number in trigonometric form r(cos theta + i sin theta) with theta in the interval [0°, 360°). 9 sqrt 3 + 9i 2.) Find the product. Write the product in rectangular form, using exact values. [4 cis 30°] [5

2. Math

   Find the exact solutions of the equation In The interval.. Sin 2x -sin x=0

3. Precalculus

   sin^2(2x)=2sinxcosx. Find all solutions to each equation in the interval [0, 2pi) So I started off changing 2sinxcosx = sin(2x), and my equation ended as sin^2(2x) = sin(2x). I subtracted sin(2x) by both sides and factored out

4. Calculus

   Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1

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