Maths-
General
Easy
Question
The length of the tangent of the curves
is
Hint:
We have to find the length of the tangent. We are given the values of x and y as function of
. We will use the formula of length of tangent to find the value.
The correct answer is: ![a sin squared invisible function application theta](data:image/png;base64,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)
The given values of x and y are as follows:
x = acos3θ
y = asin3![theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=)
The formula for length of tangent is
Length = ![open vertical bar y square root of 1 plus open parentheses fraction numerator d x over denominator d y end fraction close parentheses squared end root close vertical bar](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAAvCAYAAADpaEQxAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAeOiuv/QAABOFJREFUeNrtW11IFUEUPohIiEShUVFRiESUhFAQYVKBDyImEkEFRYlhET74IGSUWFgRBT6IGBEWESJkJIXYQ4RERA9FiZWFEhERJVJGRoWFt3O6Z2lbd++d2Z29M9p+8MH92dndO9+dmXO+OQsQHrKQsYjKOAWxEETLR76GCCoRC1u0MmRf1M/TS7Qa5KWon4XFIE4g7yPzdIl2Flkf6SGFNORB5GNdonUhd0Q6+MIPXaINI1cY1BH0D27VdO0Wvr4INiLv6hLtJ3KWIYIVIfuR6T7bf+Opyy/ougMsSCIs5DUtV4doi5HvDREsk1OPAp/t87jDVaVAWR7fL0f2sHBaoscNyAeGiNaEbAvQvgLZqXCabPIYYb3I2TpD/l0Kf2gQzEN+Ri6ScHFauA0FA9d4HTxkO6YKedrjz1ElMP194fuyo1dw/Q9VNAr3jxog2hHkFYlwm8yASn5N//pG7psKx7EUks+3va+UCHLakQ0eeVpC2yps0bqR2wwQbZCDEBE0OEaUhSGXkVqCbObXxcg7EvdUiHxpoiPyBLlWs2C0sI9KHP/WJUhI48jRDbc5GqSoNFvy3kZ8pkOhijaGzNEsGk1ZHYLHFnjkRuvA2z+thbjttNrHvXXw/Rkj2hzkuAFT42XkAcFjt3qsfTvB3T8t5CClmY+RRRXfnzGi0bT41ADRKOcplQjrr7p8TkJWOz6jxPcm5380nT7yMT2WcMRojGh7JSK2MDHqElonSsAHbQn4Ghb9nUP4edzZdpHKfPzeLMn1NnTRjnkkkM4goYEX8bAgaz1RCH+d8zMyBjYjP8FfKy6Dv3fL+Tp59IgiUYCjRTRaA/YlOcaadmIhihYDszFhkmh9nLuE1bGxGSJaTKVolLFv9whxTyoO9yPRFIm2B3nGZaEeEoiSclg0iERLrWilLuFvI0z1y7zC/YeRaKkXjUbTM0eY+wrENjTJb+xSfOO+agIFzq2lVjEs0cARjjbzeuZEvstndRB3+KORluKRRrjHmX8ujzJnvlPMbZw5yzkJ6ygSTbFo5IuVQ9zY3O0i2Bi32e/4jpLSTZFoekSr5dDfrTainq2bN8iLju+oLmRZJJoe0Sr4s/IEJ7gB/xrDFKh8l7i4zKI9Ex0R5aKVQ/LCHEoDPtre06beC4M65Zfi8wUto3NCuY1FTvb6JCdYiZy0vSfD9JZBoqnsZFVldBbSQbFhTKF8j+BJJlk8P+F+2KBtlbmKzqWyjM7KhbVtzdDWxQl+fUEy3A8bPSC3XWIhWRldUG+WUAoaN0H7OSAhdMPUUjOdoC0i2ToMkTK6IN6shWrw9xiYEtFoX8x62nPYwyXRhd0gv6MsUkYXxJu10AkaC3tos/MrTynj4P8BhzBAu+Mjkm1EyuiCeLMWRkFjCd1SDkZW8Q82DQMCUbAFmTI6EW/WC1TGoL1YlfKNUxD3K01DHQcOIpApo0vmzSZbUg7rFu0D8jnEzWLTkA3iD2DIlNEl8mYTYQkvJ9m6RbvP7WvATDSC2MMRomV0Vnjf7iPhprToeIDfoky089y+xFDRMnkKEynfTlZGZx+VybxZtzUz0UOFKRVtC7cvAHNRCMEe33VCxJu1I4NHZVHA6yozwXP4ZFlgNmhdalN0LhFv1o5Ww9yiP7gF/w9kvFmjUQMRph0WRF2QOvwGWhfxLguVuqoAAAEadEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mZW5jZWQgY2xvc2U9InwiIG9wZW49InwiPjxtcm93PjxtaT55PC9taT48bXNxcnQ+PG1uPjE8L21uPjxtbz4rPC9tbz48bXN1cD48bWZlbmNlZD48bWZyYWM+PG1yb3c+PG1pPmQ8L21pPjxtaT54PC9taT48L21yb3c+PG1yb3c+PG1pPmQ8L21pPjxtaT55PC9taT48L21yb3c+PC9tZnJhYz48L21mZW5jZWQ+PG1uPjI8L21uPjwvbXN1cD48L21zcXJ0PjwvbXJvdz48L21mZW5jZWQ+PC9tYXRoPitUXwUAAAAASUVORK5CYII=)
We will first differentiate x and y w.r.t θ and then find ![fraction numerator d x over denominator d y end fraction](data:image/png;base64,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)
Differentiating x w.r.t θ
![x space equals space a cos cubed theta
fraction numerator d x over denominator d theta end fraction equals a left parenthesis 3 cos squared theta right parenthesis fraction numerator d over denominator d theta end fraction cos theta
space space space space space space space equals 3 a cos squared theta left parenthesis negative sin theta right parenthesis
space space space space space space space equals negative 3 a cos squared theta sin theta
space space space space space space](data:image/png;base64,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)
Differentiating y w.r.t θ
![fraction numerator d y over denominator d theta end fraction equals a open parentheses 3 sin squared theta close parentheses fraction numerator d over denominator d theta end fraction left parenthesis sin theta right parenthesis
space space space space space space space equals 3 a sin squared theta cos theta](data:image/png;base64,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)
Now,
![fraction numerator d x over denominator d y end fraction equals fraction numerator d x over denominator d theta end fraction plus fraction numerator d theta over denominator d y end fraction
space space space space space space space equals negative 3 a cos squared theta sin theta space cross times space fraction numerator 1 over denominator 3 a sin squared theta cos theta end fraction
space space space space space space space equals negative 1 fraction numerator cos theta over denominator sin theta end fraction
space space space space space space space space equals negative fraction numerator 1 over denominator tan theta end fraction](data:image/png;base64,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)
We will substitute this value in the formula of length of tangent.
![L e n g t h space equals space open vertical bar y square root of 1 space plus space open parentheses fraction numerator d x over denominator d y end fraction close parentheses squared end root close vertical bar
space space space space space space space space space space space space space space equals open vertical bar a sin cubed theta square root of 1 space plus space open parentheses fraction numerator negative 1 over denominator tan theta end fraction close parentheses squared end root close vertical bar
space space space space space space space space space space space space space space equals open vertical bar a sin cubed theta square root of 1 space plus space fraction numerator 1 over denominator tan squared theta end fraction end root close vertical bar
space space space space space space space space space space space space space space equals open vertical bar a sin cubed theta fraction numerator square root of tan squared theta space plus space 1 end root over denominator square root of tan squared theta end root end fraction close vertical bar
space space space space space space space space space space space space space space equals open vertical bar fraction numerator a sin cubed theta s e c theta over denominator tan theta end fraction close vertical bar space space space space space space space space space space space space space space space space space... left parenthesis 1 space plus space tan squared A space equals space s e c squared A right parenthesis
space space space space space space space space space space space space space equals open vertical bar fraction numerator begin display style fraction numerator a sin cubed theta over denominator cos theta end fraction end style over denominator begin display style fraction numerator sin theta over denominator cos theta end fraction end style end fraction close vertical bar space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis s e c A space equals space 1 divided by cos A right parenthesis
space space space space space space space space space space space space space equals a sin squared theta
space space space
space space space space space space space space space space 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)
So, length of the tangent is asin2θ
For such questions, we should know the properties of trignometric functions and their different formulas.
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physics-
in a sine wave, position of different particles at time t =0 is sbown in figure: The equation for this wave travelling along the positive x - direction can be
![](data:image/png;base64,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)
in a sine wave, position of different particles at time t =0 is sbown in figure: The equation for this wave travelling along the positive x - direction can be
![](data:image/png;base64,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)
physics-General
physics
Aspherical planet far out in space has mas Mo and diameter Do. A particle of
falling near the surface of this planet will experience an acceleration due to gravity which is equal to
Aspherical planet far out in space has mas Mo and diameter Do. A particle of
falling near the surface of this planet will experience an acceleration due to gravity which is equal to
physicsGeneral
Maths-
If
then ![f subscript x y end subscript equals](data:image/png;base64,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)
We have used rules of indices and different formulae of differentiation to solve the question. When we find the derivative w.r.t to some variable we take another variable as consta.
If
then ![f subscript x y end subscript equals](data:image/png;base64,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)
Maths-General
We have used rules of indices and different formulae of differentiation to solve the question. When we find the derivative w.r.t to some variable we take another variable as consta.
physics
The time period of a simple pendulum on a freely moving artificial satellite is
The time period of a simple pendulum on a freely moving artificial satellite is
physicsGeneral
physics
The radius of the earth is 6400 km and g=
. In order that a body of 5 kg weights zero at the equator, the angular speed of the earth is =……rad/sec
The radius of the earth is 6400 km and g=
. In order that a body of 5 kg weights zero at the equator, the angular speed of the earth is =……rad/sec
physicsGeneral
physics-
A transverse wave is represented by
. For what value of its wavelength will the wave velocity be equal to the maximum velocity of the particle taking part in the wave propagation?
A transverse wave is represented by
. For what value of its wavelength will the wave velocity be equal to the maximum velocity of the particle taking part in the wave propagation?
physics-General
physics
If R is the radius of the earth and g the acceleration due to gravity on the earth's surface, the mean density of the earth is =……
If R is the radius of the earth and g the acceleration due to gravity on the earth's surface, the mean density of the earth is =……
physicsGeneral
physics-
If. two almost identical waves having frequencies
and
produced one after the other superposes then the time interval to obtain a beat of maxirmum intensity is .......
If. two almost identical waves having frequencies
and
produced one after the other superposes then the time interval to obtain a beat of maxirmum intensity is .......
physics-General
physics-
As shown in figure, two pulses in a string having center to center distance of 8 cm are travelling abng mutually opposite direction. If the speed of both the pulse is
s, then after 2s, the energy of these pulses will be…………
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)
As shown in figure, two pulses in a string having center to center distance of 8 cm are travelling abng mutually opposite direction. If the speed of both the pulse is
s, then after 2s, the energy of these pulses will be…………
![](data:image/png;base64,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)
physics-General
physics
As we go from the equator to the poles, the value of g…..
As we go from the equator to the poles, the value of g…..
physicsGeneral
physics
The gravitational force between two point masses
and
at separation r is given by F=
The constant K…..
The gravitational force between two point masses
and
at separation r is given by F=
The constant K…..
physicsGeneral
physics
Two point masses A and B having masses in the ratio 4:3 are seprated by a distance of 1m. When another point mass c of mass M is placed in between A and B the forces A and C is 1/3rd of the force between b and C, Then the distance C form is...m
Two point masses A and B having masses in the ratio 4:3 are seprated by a distance of 1m. When another point mass c of mass M is placed in between A and B the forces A and C is 1/3rd of the force between b and C, Then the distance C form is...m
physicsGeneral