Question: In the study of the stress at a point in a bar, the equation s = a cos 2 + bsin 2

In the study of the stress at a point in a bar, the equation s = a cos2 θ + bsin2 θ − 2t sinθ cosθ arises. Show that this equation can be written as

s = (a + b) + (a - b) cos 20 tsin

s = (a + b) + (a - b) cos 20 tsin 20. S

Step by Step Solution

★★★★★

3.38 Rating (176 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We can use the double angle formulae for cosine and sine to rewrite the equation s a cos2 ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Basic Technical Mathematics Questions!

Q:

This question is concerned with an l2S spin system. (b) By first applying the identity cos2 (A) = ½ j[l + cos(2A)], and then the identity cos (A)cos(B) = 1/2 [cos (A + B) + cos (A - B)], show...

Q:

The y-component is r sin (t + ). Using the same approach as on page 19, show that this y-component can be written more simply as -r sin (t).

Q:

A model for the height of Observatory Hill is given by 1 z = f(x, y) = (1+4x+6xy+12y2)3/2 i) Show that 47 +6ry + 12y can be written as the matrix expression 4x +6ry + 12y = (x, y)S $(3). where S is a...

Q:

PLEASE ANSWER ALL CORRECT AND SHOW ALL WORK I GIVE AMAZING REVIEWS A curve is described by the following parametric equations: x=3+ y= t2-4 Which statement best describes the curve? (1 point) O The...

Q:

In Exercises 1 - 16, plot the point given in polar coordinates and then give three different expressions for the point such that (a) r 0 and 0 (c) r > 0 and 2 9. (20, 3) In...

Q:

PLEASE ANSWER ALL CORRECT AND CLEAR WORK A curve is described by the following parametric equations: x=3+ y= t2-4 Which statement best describes the curve? (1 point) O The curve is a parabola with a...

Q:

E-Physics Tutorial Book Note: I have attached below the lesson for the 3 activities. Thank you so much for your time and effort. Activity 1. Directions: Use the right-hand rule to determine the...

Q:

All the information are in it (i) g(x) = x?(x + 5)%(x 1)(x 4) (a) Degree: ; Leading coefficient: ; based on this the end behavior is: (b) the x-intercepts: X-intercept Multiplicity Bounce or cross?...

Q:

14.1 SUMMARY . A vector-valued function is a function of the form A sample is shown fort cate with a diagram the position vectors r ( t ) = (x (1 ) . y (1), z(1) > = x(1)i + >(1)j+ z(1)k (10 - DZ + 1...

Q:

Fraction of hosts infected Case Study 2 Hosts, Parasites, and Time-Travel 0.8 0.6 0.4 0.2 0 Past Contemporary Future Time Figure \u00031 Horizontal axis is the time from which the parasite was taken,...

Q:

You run a chain of movie theaters, so you commission a marketing study that categorizes your potential customers into 10 equal-sized groups according to what theyre willing to pay for a movie ($10,...

Q:

When 10 British Army soldiers on a 10-day training exercise descended into Low's Gully, a narrow chasm that cuts through Mt. Kinabalu in Borneo, each knew "the golden rule for such expeditions -...

Q:

When you reach 6 5 , you will be enrolled in Medicare Part A and B automatically, and there will no monthly premiums to pay for both parts. True or False?

Q:

Analyze the writing for each email based on tone, style, or design.

Q:

Graph the function. Graph should contain at least two periods. Use the graph to determine the domain and the range of function. x + y = cot + 4

Q:

Graph the function. Graph should contain at least two periods. Use the graph to determine the domain and the range of function. y = -4 cot(2x)

Q:

Graph the function. Graph should contain at least two periods. Use the graph to determine the domain and the range of function. y = 4 sec (2x)

Q:

The company cost of capital for a firm with a 65/35 debt/equity split, 6.75% cost of debt, 13.75% cost of equity, and a 35% tax rate would be

Q:

Benjamin Manufacturing has a target debt-equity ratio of 0.4. Its cost of equity is 12% and its cost of debt is 7%. If the tax rate is 35%, what is the companys WACC?

Q:

Myers Business Systems is evaluating the introduction of a new product the possible levels of unit sales and the probabilities of their occurrence are given next Dababit Fossible Markt Reaction Tir...