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Xelga [282]
3 years ago
13

Find all the solutions of the given equations in the interval [0,2pi) tan^3x=tanx and cos 3x=-cos3x

Mathematics
1 answer:
slamgirl [31]3 years ago
7 0
\tan^3x=\tan x
\tan^3x-\tan x=0
\tan x(\tan^2x-1)=0
\tan x(\tan x-1)(\tan x+1)=0
\begin{cases}\tan x=0\\\tan x-1=0\\\tan x+1=0\end{cases}

\tan x=\dfrac{\sin x}{\cos x}=0\implies \sin x=0\implies x=0,\pi

\tan x-1=0\iff\tan x=1\implies x=\dfrac\pi4,\dfrac{5\pi}4

\tan x+1=0\iff\tan x=-1\implies x=\dfrac{3\pi}4,\dfrac{7\pi}4

- - -

\cos3x=-\cos3x
2\cos3x=0
\cos3x=0\implies 3x=\dfrac\pi2,3x=\dfrac{3\pi}2\implies x=\dfrac\pi6,x=\dfrac\pi2

This doesn't account for all the solutions, however; there are some values of x that push 3x outside the interval [0,2\pi), so let's take a few more:

3x=\dfrac{5\pi}2\implies x=\dfrac{5\pi}6
3x=\dfrac{7\pi}2\implies x=\dfrac{7\pi}6
3x=\dfrac{9\pi}2\implies x=\dfrac{9\pi}6
3x=\dfrac{11\pi}2\implies x=\dfrac{11\pi}6

We can stop there, since the next candidate gives

3x=\dfrac{13\pi}2\implies x=\dfrac{13\pi}6>2\pi
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suppose that two people standing 3 miles apart both see the burst from a firework display.after a period of time ,the first pers
Marrrta [24]

The fireworks display occur at 550.331 ft

The generic equation for a hyperbola provided by: is the best method for solving the problem in this instance.

\frac{y^{2} }{b^{2} } - \frac{x^{2} }{a^{2} } = 1 -

We presume that the y-axis is where the hyperbola's longer axis lies.

In this instance, the sound traveled a total of 1100 meters, and the value of a can be calculated as follows:

2a = 1100

a = 550ft

Given that the two people are 3 miles apart, we can calculate the value of c in feet as follows:  

1 mile = 5280 feet

∴ 3 miles = 15840 ft = c

And this is how we may determine what b is worth:

b^{2} = c^{2} - a^{2}

b^{2} = 15840^{2} - 550^{2}

b^{2} = 250603100

Our equation is thus given by:

\frac{y^{2} }{250603100 } - \frac{x^{2} }{550^{2} } = 1

And for this case we want to find the value of x when y = 3ft=15840ft and solving for x we get,

\frac{15840^{2} }{250603100 } - \frac{x^{2} }{550^{2} } = 1

\frac{15840^{2} }{250603100 } - 1 = \frac{x^{2} }{550^{2} }

1.001- 1 = \frac{x^{2} }{550^{2} }

0.001 = \frac{x^{2} }{550^{2} }

302865.145= {x^{2}

x = 550.331 ft.

The fireworks display occur at 550.331 ft.

Learn more about hyperbola here :

brainly.com/question/14307125

#SPJ1

8 0
2 years ago
Can someone answer this please
Ira Lisetskai [31]
I got 75 and I’m pretty sure that right?
4 0
3 years ago
Read 2 more answers
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!! I NEED TO FINISH THESE QUESTIONS BEFORE MIDNIGHT TONIGHT.
seropon [69]

Yo sup??

we can solve this question by applying trigonometric ratios

sin31=TU/TV

TV=TU/sin31

TV=7.76

=7.8

Hope this helps.

7 0
4 years ago
Charley and Sarah went to the candy store.
Pepsi [2]

Answer:

rtt6655r55

Step-by-step explanation:

4 0
4 years ago
B/5&gt;-1<br> Solve the inequality. Graph and check the solution.
Usimov [2.4K]

Answer:

b>-5

Step-by-step explanation:

\frac{b}{5}   >  - 1

Multiply by 5 to isolate b.

b  >  - 5

If you graph this on a line, it would be a hollow point facing the right, since it's any number greater than five, not including 5.

If you put any number greater than -5, you'll output greater than - 1.

4 0
3 years ago
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