Applying the Pythagorean identity and simplifying we get:
Because the two distances are the same, we set them equal to each other and simplify.
Finally we subtract
from both sides and divide both sides by
Thus, we have the difference formula for cosine. We can use similar methods to derive the cosine of the sum of two angles.
Sum and difference formulas for cosine
These formulas can be used to calculate the cosine of sums and differences of angles.
Given two angles, find the cosine of the difference between the angles.
Write the difference formula for cosine.
Substitute the values of the given angles into the formula.
Simplify.
Finding the exact value using the formula for the cosine of the difference of two angles
Using the formula for the cosine of the difference of two angles, find the exact value of
Use the formula for the cosine of the difference of two angles. We have
Find the exact value of
Finding the exact value using the formula for the sum of two angles for cosine
Find the exact value of
As
we can evaluate
as
Thus,
Find the exact value of
Using the sum and difference formulas for sine
The
sum and difference formulas for sine can be derived in the same manner as those for cosine, and they resemble the cosine formulas.
Sum and difference formulas for sine
These formulas can be used to calculate the sines of sums and differences of angles.
Given two angles, find the sine of the difference between the angles.
Write the difference formula for sine.
Substitute the given angles into the formula.
Simplify.
Using sum and difference identities to evaluate the difference of angles
Use the sum and difference identities to evaluate the difference of the angles and show that part
a equals part
b.
Let’s begin by writing the formula and substitute the given angles.
Next, we need to find the values of the trigonometric expressions.
Now we can substitute these values into the equation and simplify.
Again, we write the formula and substitute the given angles.
Next, we find the values of the trigonometric expressions.
Now we can substitute these values into the equation and simplify.
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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