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cos(phi - 1) = cos(phi)cos(1) + sin(phi)sin(1)
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How do you calculate sec in trigonometry?
sec(x)=1/cos(x) - (hint: look at the third letter: sec->(1/)cos, cosec->(1/)sin, cot->(1/)tan)
Can two non-zero vector got a zero resultant?
Yes.If the angle between them is 90 degrees. As we know that A.B=|A| |B| cos (phi). When phi=90 degree,cos 90=0. Hence A.B= |A| |B| *0 =0.
How is the golden ratio worked out?
(a+b)/a=a/b=phi (the golden ratio, as defined) (a+b)/a=phi (we'll solve this equation) 1+b/a=phi (just changing the form of the left side a little) 1+1/phi=phi (a/b=phi so b/a=1/phi) phi+1=phi2 (multiply both sides by phi) phi2-phi-1=0 (rearrange) From here, we can use the quadratic equation to find the positive solution: phi=(-b+√(b2-4ac))/(2a) phi=(1+√(1+4))/2 phi=(1+√5)/2≈1.618
How do you prove that (1 plus cotx)2-2cotx 1(1-cos)(1 plus cos)?
Manipulate normally, noting:cot x = cos x / sin xcos² x + sin² x = 1 → sin²x = 1 - cos² xa² - b² = (a + b)(a - b)1 = 1²ab = baa/(bc) = a/b/c(1 + cot x)² - 2 cot x = 1² + 2 cot x + cot² x - 2 cot x= 1 + cot² x= 1 + (cos x / sin x)²= 1 + cos² x / sin² x= 1 + cos² x / (1 - cos² x)= ((1 - cos² x) + cos² x)/(1 - cos² x)= 1/(1² - cos² x)= 1/((1 + cos x)(1 - cos x))= 1/(1 - cos x)/(1 + cos x)QED.
How do you solve sinx divided by 1 plus cosx plus cosx divided by sinx?
sin x/(1+cos x) + cos x / sin x Multiply by sin x (1+cos x) =[(sin^2 x + cos x(1+cos x) ] / sin x (1+cos x) = [(sin^2 x + cos x + cos^2 x) ] / sin x (1+cos x) sin^2 x + cos^2 x = 1 = (1+cos x) / sin x (1+cos x) = 1/sin x
Why power factor in cos phi why not in sin phi?
Because it has to be 1 when the phase angle is zero.
How do you calculate power angle of a synchronous generator?
tan (phi)= (V* sin (theta) + Ia*Xs)/(V*cos (theta) +Ia*ra) theta is power factor angle torque angle= phi-theta
Two and an half kva equals how many ampere?
2.5 kVA means 2500 VA (volt-ampere). To calculate the amperes you need the voltage. 2.5 kVA x cos (phi) = 2.5 kW (kilowatts) if phi is 0 or power factor (phi) is unity.
How do you calculate sec in trigonometry?
sec(x)=1/cos(x) - (hint: look at the third letter: sec->(1/)cos, cosec->(1/)sin, cot->(1/)tan)
Why does the rotor of an alternator at rated power dissipates more heat at a low power factor load than at a high power factor load?
Equation for power in an AC circuit is Power (P) = root3 Voltage (V) x Current (I) x power factor (cos phi) P = root3 V I Cos Phi. Value of cos phi is maximum 1. Normally 0.95 and above is considered to be good. root 3 and V assuming to be constant, if the cos phi is low, to be able to supply rated power, the system draws increased current (I). With increased current IR and copper losses increase resulting over heating of the motor.
How do you convert kva to kw and currents?
3 phase kVA = V*I*sqrt(3) Where voltage is line to line, and current is the actual RMS current flowing in the a wire. kW = V*I*sqrt(3)*Cos (phi), where phi is the angle between the voltage and current; Cos (phi) is also known as the power factor. kVA is the vector sum of kW (real power) and kVAR (reactive power). As the equations above suggest, you must know the voltage to correctly calculate the current.
Can two non-zero vector got a zero resultant?
Yes.If the angle between them is 90 degrees. As we know that A.B=|A| |B| cos (phi). When phi=90 degree,cos 90=0. Hence A.B= |A| |B| *0 =0.
Why do we use 1.73 as multiplication factor to calculate Phase to Neutral voltage?
because 3Phase power - V X I X Cos Phi X Square root of 3 and square root of 3 - 1.73
How is the golden ratio worked out?
(a+b)/a=a/b=phi (the golden ratio, as defined) (a+b)/a=phi (we'll solve this equation) 1+b/a=phi (just changing the form of the left side a little) 1+1/phi=phi (a/b=phi so b/a=1/phi) phi+1=phi2 (multiply both sides by phi) phi2-phi-1=0 (rearrange) From here, we can use the quadratic equation to find the positive solution: phi=(-b+√(b2-4ac))/(2a) phi=(1+√(1+4))/2 phi=(1+√5)/2≈1.618
What is the formula to calculate split times?
The formula to calculate split times is given by percent of time= (2-4*phi)* (percent of distance) ^2 + ((4*phi)-1) *percent of distance). Positive splits and negative splits are the two types of splits.
What is cos on an electric motor?
Cos phi is a European term used on a motor to differentiate between apparent power (kVA) of an inductive load as compared to the active power (kW) that is really used by the load. Cos phi= active power/apparent power. In North America a more familiar term would be power factor. Power factor = kW/kVA
2 cos x plus 1 cos x plus -1 equals 0?
2 cos * cos * -1 = 2cos(square) * -1 =cos(square) + cos(square) *-1 =1- sin(square) +cos(square) * -1 1 - 1 * -1 =0
