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Evaluate the Integral

Evaluate (be careful if n=m) ∫ 0 --> L sin(n pi x/L) sin(m pi x/L) dx for n>0 and m>0. Use the trigonometric identity 2 sin a sin b = cos(a-b) - cos(a+b) Please see the attached file for the fully formatted problems.

Cross-sectional Area and Co-ordinates of Holes : Algebra and Trigonometry

1. A flat is machined on a circular bar if 15 mm diameter with a central depth of 2 mm. Find the area of cross-section of the finished bar. Q2. The diagram shows 5 holes equally spaced round a pitch circle of diameter 100 mm. Calculate the co-ordinate dimensions (i.e. the x and y co-ordinates) of the hole centres relative to

Analyse a trigonometric function and graph

Q1. The figure below shows the graph of a sine function -y is a function of x, with x measured in degrees. For this function state: a. Its PERIOD b. Its AMPLITUDE c. Its PHASE SHIFT from the sine function y = sin3xo d. The equation of the function Please see attached.

Sound Waves

Consider the wave equation when the solution s admits spherical symmetry, ie, s(t,x,y,z)=v(t,r), where ... , the wave equation becomes: (1) making the substitution for some twice differentiable function h, show that (1) becomes hence, show that the general solution reads for any twice differentiable functions f

Trigonometric Equations : Solution and Area of Triangle

1. Find all the solutions of the equation 3sin20(degrees) = cos2x(degrees) in the range 0(degrees) is less then or equal to x(degrees) which is less than or equal to 180(degrees). 2. A triangle has sides A-C =3cm A-B = 5 cm B-C = 4 cm Find the area of

Sine & CoSine

Find two angles such that sin theta=.9872. Describe the steps you used on your calculator.

Trigonometric Identity

If Z1= R1(cosx1+sinxI) and Z2= (cosx2+sinxI) How do you prove that Z1 multiplied by Z2 = R1 multiplied by R2(Cos(x1+x2)+sin(x1+x2)I).

Applying Trigonometric Identities

Evaluate this expression and put in terms of sin x and/or cos x. sin6x + sin4x show your work and explain how the answer was obtained.

Evaluating Trig functions

Use the given values to evaluate the remaining trig functions. sin(-x) = -1/3, tan x = -sq. root of 2/4 Please show me the complete steps to evaluate this problem.

Limit of Trigonometric Function : L'Hopital's Rule

Lim of theta as theta approaches zero of (cos theta - 1) / sin theta Please provide a detailed, step-by-step solution so that I can understand what is happening and will be able to solve similar problems in the future on my own. Thank you.

Trigonometry : Word Problems

Q1. A glass crystal sculpture is made in the shape of a regular octagonal prism with 10 cm sides. Each of the lateral faces is square. To avoid breakage in shipment, the piece is padded with plastic foam beads when it is packed in its square-based rectangular box. The layer of beads must be at least 1 cm thick on all sides of

Trigonometry and vectors

A force of 800 lbs acts in an upward direction of 40 degrees with the floor. Draw this force as a vector and determine its horizontal and vertical components.


A handicap ramp is 5.26 meters above the ground. What will the length of the ramp if it makes an angle of 23 degrees with the floor?


A length of rope 168 feet stretches from a bolt in the floor to the peak of an 87 foot radio tower. What is the distance from the floor at the radio tower base to the bolt? What angle does the rope make with the floor?