1. O

    Finding the second derivative of trig function

    Hi, I hope someone can help. I'm trying to find the second derivative for the trigonometric function y = sinxtanx Apparently the first derivative is y' = sinx + secxtanx even though I got y' = cosxtanx + sinx(secx)^2. I must of missed a step and would appreciate help. The second derivative...
  2. O

    Characteristics of combined functions

    Hi, I hope someone can help. I'm hoping that someone help me understand combined function characteristics with the following examples: 1. y=2^x-x^3 would this function not have a relative maximum at x = 0.59? Would it also have a minimum at x = 8.177? 2. y = sin(2pix) - 2sin(pix) my textbook...
  3. O

    Simplifying trigonometric expression

    Hi, I hope someone can help me properly simplify the following expression: The solution is apparently Sincerely, Olivia
  4. W

    Problems in three dimensions

    Standing due south of a tower 50m high, the angle of elevation of the top is 26o. What is the angle of elevation after walking a distance of 120m due east?
  5. J

    Continuous Function

    (cos x)/(x - (pi/2)) I don't Understand why this function is continuous because when I plug pi/2 in x, it causes problems.
  6. T

    Simplifying a trigonometric function

    How does -sin²(x+y) simplify to -x²/x²+1?
  7. C

    Trigonometric Formula

    I have a question about one of the Trig formulas. I know sin^2(x)=\frac{1}{2}(1-\cos{(2x)}) I’m wondering if this formula works for any real number for the coefficient in the argument for sin(x)? If so would it look like this? sin^2{(\alpha{x})}=\frac{1}{2}(1-=cos^2{({2}\alpha{x})}) Or...
  8. K


    According to my book: cos115+cos25=!/2(cos(115+25)+cos(115-25)) I think this is a typo. Is there a way of getting this formula? May be it meant cos115.cos25
  9. U

    Trigonometric Substitution...6

    Let S be the integral symbol. Integrate [root(25-x^2)]/(x) dx Note: x is given to be 5sinθ. I am having fun solving these integrals involving trigonometric substitution but hate getting stuck somewhere along the way. dx = 5cosθdθ I drew my right triangle and labelled each leg and...
  10. U

    Trigonometric Substitution...5

    I need help with this integral. The 4x^2 in the radicand threw me off a little bit. Do we have to complete the square in the radicand to make integration possible? I know that a = 3. x = 3tanθ dx = 3sec^2 θdθ When drawing the right triangle, the hypotenuse is root{x^2+9}. There...
  11. U

    Trigonometric Substitution...4

    Integrate -5x/(x^2+5)^(3/2) dx Let S = integral symbol -5 S x/[root(x^2+5)]^3 dx x = root(5)tanθ dx = root(5)sec^2 θ dθ Can I get the next three steps? I can take it from there. Thanks.
  12. U

    Trigonometric Substitution...3

    Integrate [root(1-x^2)]/(x^4) dx Let S = integral symbol x = asinθ I know a = 1. Thus, x = sinθ. So, dx = cosθdθ I now plug into given integral. S = [root{1-(sinθ)^2}]/(sinθ)^4 cosθdθ After simplifying some more, I ended up with the following integral: S (cos^2...
  13. I

    trigonometric equation

    If: sin(x+y)=k Find sin(2x)=? I did this: I)sen2x=2senx.cosx II)sen²x+cos²x=1 (senx+cosx)²-2senxcox=1 (senx+cosx)²-sen2x=1 (senx+cosx)² -1=sen2x Considering cosx=y (senx+y)² -1=sen2x sen²x+2senx.y+y²-1=sen2x Help?
  14. U

    Trigonometric Substitution...2

    Let S = integral symbol Let t = theta S 1/(25 - x^2)^(3/2) dx We are given x to be 5sint. I found dx to be 5costdt. I drew my right triangle and labeled each leg and hypotenuse accordingly. To be honest, the fractional exponent in the denominator threw me in for a loop. I know the...
  15. U

    Trigonometric Substitution...1

    Integrate (x^3)*root(x^2 - 4) We are given x = 2 sec(theta). I found dx to be 2sec(theta)tan(theta) d(theta). I drew my right triangle and labeled each leg and hypotenuse accordingly. Let S = integral symbol Let t = theta S (sect)^3 * [root(4sec^2t] * 2sect * tant dt After further...
  16. U

    Trigonometric Integrals...4

    Integrate sin^2 x cos^2 x dx I decided to raise (sinxcosx) to the second power because it is an equivalent integral to the one given. I know the double angle identity sin2x = 2sinxcosx. I divided both sides by 2 to get (1/2)sin2x = sinxcosx. The integral now looks like this...
  17. U

    Trigonometric Integrals...3

    Integrate sec^4 (5x) dx I separated into two even power integrals. sec^2 (5x) sec^2 (5x) dx I then let one of the secants be [1 + tan^2 (5x)]. The integral now looks like this sec^2 (5x) (1 + tan^2 (5x)) dx I then let u = tan(5x) to find that dx = du/5sec^2(5x). The...
  18. U

    Trigonometric Integrals...2

    Integrate x*sin^2 x dx Here we have x times a trigonometric function. I used integration by parts to find the answer (1/8)[2x^2 - 2sin(2x) - cos(2x) + C. This answer is slightly different than the textbook. In the textbook the answer is (1/8)[ 2x2 - 2x*sin(2x) - cos(2x) + C. The second...
  19. U

    Trigonometric Integrals...1

    Integrate cos^3 x * sin x dx I broke the cosine function into two parts: cos^2 x * cos x The integral now looks like this: cos^2 x * sin x * cos x dx I then let cos^2 x = 1 - sin^2 x. Here is the integral now: (1 - sin^2 x) * sin x * cos x dx I let u = sin x making du = cos x dx. The...
  20. I

    trigonometric function

    Given the following information: f(x)=-sinx g(x)=cosx find x(s) in order to have f=g Thanks in advance!