Solve this system of trigonometric equations [closed]

-1

How to solve this system of equations analytically?

$$
begin{cases}
:9tanalpha -frac{4.9cdot 9^2}{v^2cos^2alpha }=2.1\
:23tanalpha :-frac{4.9cdot :23^2}{v^2cos^2alpha :}=2.44
end{cases}
$$

edited Nov 30 at 16:17

KM101

4,173417

asked Nov 30 at 16:14

Stepii

106

closed as off-topic by GNUSupporter 8964民主女神地下教會, Brahadeesh, Vidyanshu Mishra, amWhy, Jyrki Lahtonen Dec 1 at 21:11

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神地下教會, Brahadeesh, Vidyanshu Mishra, amWhy, Jyrki Lahtonen

If this question can be reworded to fit the rules in the help center, please edit the question.

Thanks for the catch! Is the procedure clear now? Or is any clarification needed?
– KM101
Nov 30 at 17:08

@KM101 Thanks, now everything is clear!
– Stepii
Nov 30 at 17:12

Glad to have helped!
– KM101
Nov 30 at 17:13

add a comment |

-1

How to solve this system of equations analytically?

$$
begin{cases}
:9tanalpha -frac{4.9cdot 9^2}{v^2cos^2alpha }=2.1\
:23tanalpha :-frac{4.9cdot :23^2}{v^2cos^2alpha :}=2.44
end{cases}
$$

edited Nov 30 at 16:17

KM101

4,173417

asked Nov 30 at 16:14

Stepii

106

closed as off-topic by GNUSupporter 8964民主女神地下教會, Brahadeesh, Vidyanshu Mishra, amWhy, Jyrki Lahtonen Dec 1 at 21:11

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神地下教會, Brahadeesh, Vidyanshu Mishra, amWhy, Jyrki Lahtonen

If this question can be reworded to fit the rules in the help center, please edit the question.

Thanks for the catch! Is the procedure clear now? Or is any clarification needed?
– KM101
Nov 30 at 17:08

@KM101 Thanks, now everything is clear!
– Stepii
Nov 30 at 17:12

Glad to have helped!
– KM101
Nov 30 at 17:13

add a comment |

-1

How to solve this system of equations analytically?

$$
begin{cases}
:9tanalpha -frac{4.9cdot 9^2}{v^2cos^2alpha }=2.1\
:23tanalpha :-frac{4.9cdot :23^2}{v^2cos^2alpha :}=2.44
end{cases}
$$

edited Nov 30 at 16:17

KM101

4,173417

asked Nov 30 at 16:14

Stepii

106

How to solve this system of equations analytically?

$$
begin{cases}
:9tanalpha -frac{4.9cdot 9^2}{v^2cos^2alpha }=2.1\
:23tanalpha :-frac{4.9cdot :23^2}{v^2cos^2alpha :}=2.44
end{cases}
$$

trigonometry systems-of-equations nonlinear-system

edited Nov 30 at 16:17

KM101

4,173417

asked Nov 30 at 16:14

Stepii

106

edited Nov 30 at 16:17

KM101

4,173417

asked Nov 30 at 16:14

Stepii

106

edited Nov 30 at 16:17

KM101

4,173417

edited Nov 30 at 16:17

KM101

4,173417

edited Nov 30 at 16:17

KM101

4,173417

asked Nov 30 at 16:14

Stepii

106

asked Nov 30 at 16:14

Stepii

106

asked Nov 30 at 16:14

Stepii

106

closed as off-topic by GNUSupporter 8964民主女神地下教會, Brahadeesh, Vidyanshu Mishra, amWhy, Jyrki Lahtonen Dec 1 at 21:11

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神地下教會, Brahadeesh, Vidyanshu Mishra, amWhy, Jyrki Lahtonen

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by GNUSupporter 8964民主女神地下教會, Brahadeesh, Vidyanshu Mishra, amWhy, Jyrki Lahtonen Dec 1 at 21:11

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神地下教會, Brahadeesh, Vidyanshu Mishra, amWhy, Jyrki Lahtonen

If this question can be reworded to fit the rules in the help center, please edit the question.

Thanks for the catch! Is the procedure clear now? Or is any clarification needed?
– KM101
Nov 30 at 17:08

@KM101 Thanks, now everything is clear!
– Stepii
Nov 30 at 17:12

Glad to have helped!
– KM101
Nov 30 at 17:13

add a comment |

Thanks for the catch! Is the procedure clear now? Or is any clarification needed?
– KM101
Nov 30 at 17:08

@KM101 Thanks, now everything is clear!
– Stepii
Nov 30 at 17:12

Glad to have helped!
– KM101
Nov 30 at 17:13

Thanks for the catch! Is the procedure clear now? Or is any clarification needed?
– KM101
Nov 30 at 17:08

@KM101 Thanks, now everything is clear!
– Stepii
Nov 30 at 17:12

Glad to have helped!
– KM101
Nov 30 at 17:13

add a comment |

1 Answer
1

active

oldest

votes

Let $x = v^2cos^2alpha$ and $y = tanalpha$.

For the first equation:

$$9y-frac{4.9(9^2)}{x} = 2.1 implies 9xy-396.9 = 2.1x implies 9xy-2.1x = 396.9$$

$$implies x(9y-2.1) = 396.9 implies color{blue}{x = frac{396.9}{9y-2.1}}tag{1}$$

For the second equation:

$$23y-frac{4.9(23^2)}{x} = 2.44 implies 23xy-2592.1 = 2.44x implies 23xy-2.44u = 2592.1$$

$$x(23y-2.44) = 2592.1 implies color{green}{x = frac{2592.1}{23y-2.44}}tag{2}$$

So now, you have equations $(1)$ and $(2)$.

$$color{blue}{x} = color{green}{x}$$

$$implies frac{396.9}{9y-2.1} = frac{2592.1}{23y-2.44}$$

Solve for $y$, obtain $alpha$, solve for $x$, then plug $alpha$ in $x = v^2cos^2a$ to get $v$.

edited Nov 30 at 17:06

answered Nov 30 at 16:39

KM101

4,173417

add a comment |

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

Let $x = v^2cos^2alpha$ and $y = tanalpha$.

For the first equation:

$$9y-frac{4.9(9^2)}{x} = 2.1 implies 9xy-396.9 = 2.1x implies 9xy-2.1x = 396.9$$

$$implies x(9y-2.1) = 396.9 implies color{blue}{x = frac{396.9}{9y-2.1}}tag{1}$$

For the second equation:

$$23y-frac{4.9(23^2)}{x} = 2.44 implies 23xy-2592.1 = 2.44x implies 23xy-2.44u = 2592.1$$

$$x(23y-2.44) = 2592.1 implies color{green}{x = frac{2592.1}{23y-2.44}}tag{2}$$

So now, you have equations $(1)$ and $(2)$.

$$color{blue}{x} = color{green}{x}$$

$$implies frac{396.9}{9y-2.1} = frac{2592.1}{23y-2.44}$$

Solve for $y$, obtain $alpha$, solve for $x$, then plug $alpha$ in $x = v^2cos^2a$ to get $v$.

edited Nov 30 at 17:06

answered Nov 30 at 16:39

KM101

4,173417

add a comment |

Let $x = v^2cos^2alpha$ and $y = tanalpha$.

For the first equation:

$$9y-frac{4.9(9^2)}{x} = 2.1 implies 9xy-396.9 = 2.1x implies 9xy-2.1x = 396.9$$

$$implies x(9y-2.1) = 396.9 implies color{blue}{x = frac{396.9}{9y-2.1}}tag{1}$$

For the second equation:

$$23y-frac{4.9(23^2)}{x} = 2.44 implies 23xy-2592.1 = 2.44x implies 23xy-2.44u = 2592.1$$

$$x(23y-2.44) = 2592.1 implies color{green}{x = frac{2592.1}{23y-2.44}}tag{2}$$

So now, you have equations $(1)$ and $(2)$.

$$color{blue}{x} = color{green}{x}$$

$$implies frac{396.9}{9y-2.1} = frac{2592.1}{23y-2.44}$$

Solve for $y$, obtain $alpha$, solve for $x$, then plug $alpha$ in $x = v^2cos^2a$ to get $v$.

edited Nov 30 at 17:06

answered Nov 30 at 16:39

KM101

4,173417

add a comment |

Let $x = v^2cos^2alpha$ and $y = tanalpha$.

For the first equation:

$$9y-frac{4.9(9^2)}{x} = 2.1 implies 9xy-396.9 = 2.1x implies 9xy-2.1x = 396.9$$

$$implies x(9y-2.1) = 396.9 implies color{blue}{x = frac{396.9}{9y-2.1}}tag{1}$$

For the second equation:

$$23y-frac{4.9(23^2)}{x} = 2.44 implies 23xy-2592.1 = 2.44x implies 23xy-2.44u = 2592.1$$

$$x(23y-2.44) = 2592.1 implies color{green}{x = frac{2592.1}{23y-2.44}}tag{2}$$

So now, you have equations $(1)$ and $(2)$.

$$color{blue}{x} = color{green}{x}$$

$$implies frac{396.9}{9y-2.1} = frac{2592.1}{23y-2.44}$$

Solve for $y$, obtain $alpha$, solve for $x$, then plug $alpha$ in $x = v^2cos^2a$ to get $v$.

edited Nov 30 at 17:06

answered Nov 30 at 16:39

KM101

4,173417

Let $x = v^2cos^2alpha$ and $y = tanalpha$.

For the first equation:

$$9y-frac{4.9(9^2)}{x} = 2.1 implies 9xy-396.9 = 2.1x implies 9xy-2.1x = 396.9$$

$$implies x(9y-2.1) = 396.9 implies color{blue}{x = frac{396.9}{9y-2.1}}tag{1}$$

For the second equation:

$$23y-frac{4.9(23^2)}{x} = 2.44 implies 23xy-2592.1 = 2.44x implies 23xy-2.44u = 2592.1$$

$$x(23y-2.44) = 2592.1 implies color{green}{x = frac{2592.1}{23y-2.44}}tag{2}$$

So now, you have equations $(1)$ and $(2)$.

$$color{blue}{x} = color{green}{x}$$

$$implies frac{396.9}{9y-2.1} = frac{2592.1}{23y-2.44}$$

Solve for $y$, obtain $alpha$, solve for $x$, then plug $alpha$ in $x = v^2cos^2a$ to get $v$.

edited Nov 30 at 17:06

answered Nov 30 at 16:39

KM101

4,173417

edited Nov 30 at 17:06

answered Nov 30 at 16:39

KM101

4,173417

answered Nov 30 at 16:39

KM101

4,173417

answered Nov 30 at 16:39

KM101

4,173417

add a comment |

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