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OTRIGONOMETRIC FUNCTIONS Writing the equation of a sine or cosine function given its graph.... write an...
Write the equation of a sine or cosine function to describe the graph. a TT 2x SA 3 2 3 6
O POLYNOMIAL AND RATIONAL FUNCTIONS Writing the equation of a rational function given its graph 3 . The figure below shows the graph of a rational functionſ. It has vertical asymptotes x -1 and x=6, and horizontal asymptote y The graph has x-intercept 4, and it passes through the point (2, -1). The equation for f(x) has one of the five forms shown below. Choose the appropriate form for f (x), and then write the equation. You can assume that...
Write an equation of the form y= a sin bx or y= a cosbx to describe the graph below. 0 . 0/0 JT sin cos 25 Se -1- X -24 5 ?
Given The partial graph of the cosine function below has a minimum post -2 nd a maximum point at C ) as shown below. The equation of the function can be expressed in the form acos -c))+d. ...c.d w . a) Draw the midline on the graph. b) What is the amplitude of the graph? c) What is the period of the graph? d) What is the value of b in the above equation? e) What is the phase shift...
4. (a) Expand the given function in an appropriate cosine or sine series. (x) , , -1<x<0 05x< (6 marks) (b) Find the product solutions for the given partial differential equation by using separation of variables. U, +3u, = 0 (6 marks)
Use identities to find values of the sine and cosine functions of the function for the angle measure. V2 20, given sin 0 = and cos 0 >0 5 cos 20 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) sin 20=0 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Write an equation of the form y= a sin bx or y = a cosbx to describe the graph below. 0/0 3 2 л sin cos 1- - 42 -22 25 42 67 81 10, 12: O=O -2- х 5 ?
5. Write an equation of the form S(x)-Asin(ar + +8 for the sine function whose graph is shown below Equation 6. Graph the oriented angle-in standard position. Findtwo coterminal angles, one of which is positive and the other negative. It is not necessary to graph the coterminal angles, but state their measures in radians below. Positive coter minal angle Negative coterminal angle
Expand each function into its cosine series and sine series representations of the indicated period T. Determine the values to which each series converges to at x = 0, x 2 and x =-2. b)f(x)= e. T=2π 0S2 2.2Sx<3 T=6
Expand each function into its cosine series and sine series representations of the indicated period T. Determine the values to which each series converges to at x = 0, x 2 and x =-2. b)f(x)= e. T=2π 0S2 2.2Sx
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform 10<tsI g(t) = le-3, +1 , 1<t 2 .22 Q2 Use Laplace transform to solve the following initial value problem: yty(o)-0 and y (0)-2 A function f(x) is periodic of period 2π and is defined by Q3 Sketch the graph of f(x) from x-2t to2 and prove that 2sinh π11 f(x)- Q4 Consider the function f(x)=2x, 0<x<1 Find the a Fourier cosine series b)...