1 answer

How do you find all solutions of the equation #sin(x+pi/4)-sin(x-pi/4)=1# in the interval #[0,2pi)#?

Question:

How do you find all solutions of the equation #sin(x+pi/4)-sin(x-pi/4)=1# in the interval #[0,2pi)#?

Answers

#"The Soln. Set.="{2kpi+-pi/4 | k in ZZ.}.#

The Solns. in #[0,2pi), are, therefore, pi/4, and, 7pi/4.#

Explanation:

#sin(x+pi/4)-sin(x-pi/4)=1.#

#rArr 2cos[1/2{(x+pi/4)+(x-pi/4)}]sin[1/2{(x+pi/4)-(x-pi/4)}]=1.#

#rArr 2cosxsin(pi/4)=1.#

#rArr2*1/sqrt2*cosx=1.#

#rArr cosx=1/sqrt2=cos(pi/4).#

Knowing that, #costheta=cosalpha rArr theta=2kpi+-alpha, k in ZZ,#

#"The Soln. Set.="{2kpi+-pi/4 | k in ZZ.}.#

In Particular, the Solns. in #[0,2pi), are, therefore, pi/4, and, 7pi/4.#

.

Similar Solved Questions

1 answer
Answer All Questions. (9) Let f(x,y) = 1+ 4- y2. Evaluate f(3,1), find and sketch the...
Answer All Questions. (9) Let f(x,y) = 1+ 4- y2. Evaluate f(3,1), find and sketch the domain of f. (10) A thin metal plate, located in the xy-plane, has temperature T(x,y) at the point (x,y). The level curves of T are called isothermals because at all points on such a curve the temperature is the sa...
1 answer
How to write a patient note regarding wound care on the sacrum and packing the wound
How to write a patient note regarding wound care on the sacrum and packing the wound...
1 answer
Please answer and show work!! 4) A 1kg object is moving with a velocity of 6...
Please answer and show work!! 4) A 1kg object is moving with a velocity of 6 m/s to the right. It collides and sticks to a 2kg object moving with a velocity of 3 m/s in the same direction kinetic energy is lost in the collision? 5) A 2kg mass moving with a velocity of 7 m/s collides elastic ally w...
1 answer
How do you find the sum of the infinite geometric series 9+6+4+...?
How do you find the sum of the infinite geometric series 9+6+4+...?...
1 answer
STS Some updates Homework: Lecture 2 Homework Score: 0 of 1 pt Hep D. Working E....
STS Some updates Homework: Lecture 2 Homework Score: 0 of 1 pt Hep D. Working E. Sleeping O A. Students spend the majorty of their Sime on socialiring or recreation, but heir time on atending class or studying on sleeping....
1 answer
5. Which of the following techniques would be most appropriate for facilitating initiation of movement in...
5. Which of the following techniques would be most appropriate for facilitating initiation of movement in a paretic upper extremity? a. Slow reversals b. Alternating isometrics c. Rhythmic initiation d. Agonistic reversal...
3 answers
How much energy is consumed by a 1.00 Kilowatt hair dryer used for 13.0min and a...
How much energy is consumed by a 1.00 Kilowatt hair dryer used for 13.0min and a 11.0 Watt night light that was left on for 21.0 hours?...
1 answer
Better electronic answer format, thank you! 7. Effect of a tax on buyers and sellers The...
Better electronic answer format, thank you! 7. Effect of a tax on buyers and sellers The following graph shows the daily market for wine. Suppose the government institutes a tax of $46.40 per bottle. This places a wedge between the price buyers pay and the price sellers receive. Supply Tax We...
2 answers
In a period of increasing prices which inventory flow assumption will result in the lowest...
In a period of increasing prices which inventory flow assumption will result in the lowest amount of income tax expense?...
1 answer
16 Consider a hypothetical X*-Y ion pair for which the equilibrium interionic spacing and bonding energy...
16 Consider a hypothetical X*-Y ion pair for which the equilibrium interionic spacing and bonding energy values are 0.38 nm and-6.13 eV,...
1 answer
How do you identify the degree of each term of the polynomial and the degree of the polynomial # 3w - 6w^2 + 4#?
How do you identify the degree of each term of the polynomial and the degree of the polynomial # 3w - 6w^2 + 4#?...
1 answer
A wire carries a current of 1.25 A from point A to point B in a...
A wire carries a current of 1.25 A from point A to point B in a zigzag path shown by the solid line in a uniform magnetic field of 0.250 T as shown below. What is the magnitude of the total force on the wire? 35.0° 50 cm 20 cm A A 0.174 N c B 0.219 N OC None of these answers D. 0.303 N E. 0.125 ...
1 answer
Please provide full solution with clear explanation for the following: A square conducting loop of side...
Please provide full solution with clear explanation for the following: A square conducting loop of side 4 cm lies on the z-0 plane and is centered at the origin. If it carries a current 5 mA in the counterclockwise direction, find H at the center of the loop....
1 answer
A disk of mass M and radius R is on the horizontal table, and an external...
A disk of mass M and radius R is on the horizontal table, and an external force F is applied to the disk as shown in Figure above. The coefficient of friction between the disk and the table is and it is large enough that the disk is rolling without slipping. The initial velocity of the center of mas...
1 answer
A patient is classified as having gestational diabetes if their average glucose level is above 140...
A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucos...
1 answer
Please help me to prepare a statement of cash flows using the indirect method Thank you...
Please help me to prepare a statement of cash flows using the indirect method Thank you Problem 17-09A Condensed financial data of Cheng Inc. follow. CHENG INC Comparative Balance Sheets December 31 Assets 2020 2019 Cash $105,400 $48,900 Accounts receivable 91,000 33,700 Inventory 111,400 101,900 Pr...
1 answer
1- Draw shear and bending moment diagrams for the following simply supported beams, find the location...
1- Draw shear and bending moment diagrams for the following simply supported beams, find the location and magnitude of maximum moment for each one. Show all of your calculations. 1 kN 4 KN 2 kN (7marks) 5 kN/m TITIT 40 70 70 40 40 60 A B с TI G DE All distances in cm II- 3kN 1.5 kN/m A B l...
1 answer
Question 35 On January 1, 2015, Bose Company issued bonds with a face value of $600,000....
Question 35 On January 1, 2015, Bose Company issued bonds with a face value of $600,000. The bonds carry a stated interest of 7% payable each January 1. Prepare the journal entry for the issuance assuming the bonds are issued at 95. (Credit account titles are automatically indented when the amount i...