By using the Euler's identity: ei(theta) = cos(theta) + i*(sin(theta)) Show that 1. cos(theta) = (1/2)(ei(theta) + e-i(theta)) 2. sin(theta) = (1/2i)(ei(theta) - e-i(theta)) 3. cos(A-B) = cos(A)cos(B) + sin(A)sin(B) 4. sin(A-B) = sin(A)cos(B) - cos(A)sin(B)
Q: A compound containing An+ cations and XO4- anions crystallizes in a cubic lattice. The Ant cations…
A: In this cubic structure, cations are present in the cube's corners.Therefore, the number of cations…
Q: Preliminary Problems (Pay attention to decimal places and significant figures in your calculations)…
A:
Q: What kind of decay, if any, would you expect for the nuclei with the energy-level diagrams shown in…
A:
Q: Consider a binary star system that has bright lines at 656.72 and 656.86 nm,56.46-nm hydrogen line…
A: Given that, Wavelengths are 656.72 and 656.86 nm.Also we have hydrogen line 56.46nm in rest frame.
Q: Gamma rays are emitted by the hottest and most energetic objects in the universe. Based on that…
A: Gamma rays are emitted by hottest and most energetic objects in the universe. That means the emitted…
Q: A closed system consisting of 10 kg of a gas undergoes a process during which the relationship…
A:
Q: 26. A certain hydrometer has a scale of 1cm (g/cm³). It is being used to measure the density of two…
A: A certain hydrometer has a scale of 1cm (g/cm³). It is being used to measure the density of two…
Q: Moving mirror M₂ of a Michelson interferometer a distance of 100 um causes 500 bright-dark-bright…
A: Distance d=100number of fringe N=500
Q: Which of the following is least reasonable regarding the concept of a habitable zone? Group of…
A: "In the course of millions of years, our habitable zone will slowly shift from Earth to Mars."This…
Q: 1 = A unit mass hangs in equilibrium from a spring with constant k F(t) = 3 sint is applied to the…
A:
Q: 2. Three objects are connected as shown in the figure. The strings and frictionless pulleys have…
A: Newton's second law:According to this law, the net force on an object is equal to the product of its…
Q: The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 51 km/s.…
A:
Q: Q1. A uniform beam, 2.20 m long with mass m = 25.0 kg, is mounted by a small hinge on a wall. The…
A: A system will remain in equilibrium if the following two conditions are satisfied,(i) The net force…
Q: A carousel is initially at rest. At t=0, it is given a constant angular acceleration, alpha=0.5…
A:
Q: Suppose you're experimenting with the spectrum produced by heated hydrogen gas. If you double the…
A: In this scenario, when you double the quantity of hydrogen and examine the resulting spectral lines,…
Q: Assume the Galilean transformation equations are true. Suppose that construction crews have set up a…
A: A pair of blinking lights are kept at60m apart to mark a construction zone along a road.A car moves…
Q: a satellite of mass 220.0 kg revolves in a circular orbit around the earth at on altitude 640.0 km…
A:
Q: 1.10-mm A 10.0 cm B segment D 15.0 A 52.8 nT out of the plane of the figure 52.8 nT into the plane…
A:
Q: Find DFT for the sequence [ 0.5 1 1.5-2] using FFT.
A: The FFT algorithm works by recursively dividing the input sequence into smaller sub problems and…
Q: Three charges are arranged at the corners of an iscoceles triangle with equal sides 5a and unequal…
A:
Q: Indirect Measurement 3 instruments for every basic process variables • description and operation…
A: In the field of Instrumentation and Control, indirect measurement is a technique where the value of…
Q: Let F be the fluid force (in Newtons) on a side of a semicircular plate of radius r = 6 meters,…
A:
Q: When you calculate the density of a cylinder 8.20 cm long and 0.313 cm in diameter (not radius)…
A:
Q: Two individuals are attempting to relocate a sofa by applying forces in the indicated directions. If…
A:
Q: A rectangular coil consists of N = 160 closely wrapped turns and has dimensions a = 0.400 m and b=…
A: The torque exerted on a current-carrying rectangular coil in a magnetic field is given by the…
Q: QUESTION 15 The volume of a sphere of radius R, is: V 4 =- *R zD3 How many significant digits should…
A: When we multiply or divide by some numbers, we always have to choose the number which has the least…
Q: 8. Consider a cantilever viewing platform extending over the rim of a cliff as shown below. In an…
A: Given,
Q: 22. (II) Two long parallel wires 8.20 cm apart carry A currents in the same direction. Determine the…
A:
Q: A nitrogen molecule (N2) vibrates with energy identical to a single particle of mass m = 1.162 x…
A:
Q: Uniformly charged insulating rods of length 14.0 cm (blue) and 7.0 cm (red) are bent into the shape…
A: The electric potential at the center of a uniformly charged semi-circular ring is given by the…
Q: A loudspeaker in a parked car is producing sound whose frequency is 20840 Hz. A healthy young person…
A: To solve this problem, we can use the formula for the Doppler effect:Where:
Q: Which of the following is least reasonable regarding energy production in the Sun? Group of answer…
A: The statement that is least reasonable regarding energy production in the Sun is:"Although the Sun…
Q: Here is a graph of position vs. time for two objects (dotted line and dashed line) involved in a…
A: It is Distance time graph of two object moving in same direction. Some observations from graphs are…
Q: The figure shows the paths of two bodies that leave the ground with the same initial speed vo but…
A:
Q: Charge Q is uniformly distributed along a thin, flexible rod of length L. The rod is then bent into…
A: To find the expression for the electric field at the center of the semicircle, we can break down…
Q: A Gaussian cube having sides length 12.0 cm is in a region of constant 215,000 N/C electric field as…
A: Electric field magnitude () = 215,000 N/CCube side length = 12.0 cm = 0.12 mAngle of incidence () =…
Q: Which of the following is least reasonable regarding the mass of stars? Group of answer choices…
A: Stars are of different sizes and they have their own set of characteristics based on multiple…
Q: A force of 5 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring,…
A: (a) Given values:The equation of motion can be expressed as: Simplifying, we get: The characteristic…
Q: In what ways does the birefringence property of materials affect the polarization of light?
A: Birefringence, also known as double refraction, is a property of anisotropic materials that causes…
Q: (a) Explain why some atoms are paramagnetic and others are diamagnetic with reference to the…
A: Atoms exhibit different magnetic properties due to their electronic structure and the behavior of…
Q: In the figure three identical conducting spheres initially have the following charges: sphere A, 2Q;…
A: When two spheres 1 and 2, with charge and, the new charge on each sphere is:The magnitude of the…
Q: A Michelson interferometer uses red light with a wavelength of 656.45 nm from a hydrogen discharge…
A: Wavelength Shifting length Number of fringes
Q: Calculate the wavelengths in air at 20°C for sounds in the maximum range of human hearing. The speed…
A:
Q: Consider a binary star system that has bright lines at 656.72 and 656.86 nm. Assume that the stars…
A: Given that, Wavelengths are 656.72 and 656.86 nm.
Q: A water trough has a semicircular cross section with a radius of 0.3 m and a length of 1 m (see…
A: Work-Energy Theorem:According to work-energy theorem, the change in the energy of an object is equal…
Q: (Figure 1) shows two masses hanging from a steel wire. The mass of the wire is 59.0 g. A wave pulse…
A: We will first find the tension in the horizontal part of wire using free body diagram. We then write…
Q: A football field has 60,000 square feet. Convert this to square meters. (1 inch = 2.54 cm) O 505.89…
A: To convert square feet to square meters, you can use the conversion factors:
Q: The figure below shows an infinite wire carrying current i₁ = 4.069 A coming out of the page and…
A: Magnetic field due to a long wire:The magnetic field () at a radial distance from a long carrying…
Q: A substance weighs 2 lbs in air and 1lb in water. What is its weight in the moon in pounds if it is…
A: To solve this problem, we can use the principle of buoyancy. The buoyant force on an object…
Q: Suppose that a liquid of pure component A is in equilibrium with its own vapor at a temperature T…
A: The flux of atoms at a liquid-vapor interface can be described using kinetic theory and the concept…
By using the Euler's identity:
ei(theta) = cos(theta) + i*(sin(theta))
Show that
1. cos(theta) = (1/2)(ei(theta) + e-i(theta))
2. sin(theta) = (1/2i)(ei(theta) - e-i(theta))
3. cos(A-B) = cos(A)cos(B) + sin(A)sin(B)
4. sin(A-B) = sin(A)cos(B) - cos(A)sin(B)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
