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Find all solutions to cosx cos3 x-sinx sine3x= 0 on the interval {0,2pi}

fomenos

$\bf \textit{Sum and Difference Identities}
\\ \quad \\
sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
\boxed{cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}})}
\\ \quad \\
cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}})\\\\
------------------------$

$\bf cos(x)cos(3x)-sin(x)sin(3x)=0\implies cos(x+3x)=0
\\\\\\
cos(4x)=0\implies cos^{-1}[cos(4x)]=cos^{-1}(0)\implies 4x=cos^{-1}(0)
\\\\\\
4x=
\begin{cases}
\frac{\pi }{2}\\\\
\frac{3\pi }{2}
\end{cases}\implies 
\begin{cases}
4x=\cfrac{\pi }{2}\implies &\measuredangle x=\cfrac{\pi }{8}\\\\
4x=\cfrac{3\pi }{2}\implies &\measuredangle x=\cfrac{3\pi }{8}
\end{cases}$

5 0

3 years ago

THERE ARE 8 ROWS OF CHAIRS IN THE AUDITORIUM. THREE OF THE ROWS ARE EMPTY. WHAT FRACTION OF THE ROWS ARE EMPTY?

MissTica

3 rows are empty so th fraction would be
3/8

6 0

4 years ago

What is a third in 420

kolezko [41]

420/3 = 140 rubies
Since they use 20 rubies you would do the total amount of rubies by 20.
140/20 = 7

7 0

3 years ago

Javier has four cylindrical models. The heights, radii, and diagonals of the vertical cross-sections of the models are shown in

Sever21 [200]

Given the heights, radii, and diagonals of the vertical cross-sections of the models, the model in which the lateral surface meet the base at a right angle is the model in which the height, the diameter and the diagonal of the vertical cross-section forms a right triangle.

i.e. the sum of the squares of the height (h) and the diameter (d) gives the square of the diagonal vertical cross-section (l).

For model 1:

radius: 14 cm, thus diameter = 2(14) = 28 cm
height: 48 cm
diagonal: 50 cm

 $d^2+h^2=28^2+48^2 \\ \\ =784+2,304=3,090\neq50^2=l^2$

Thus, the lateral surface of model 1 does not meets the base at right angle.

For model 2:

radius: 6 cm, thus diameter = 2(6) = 12 cm
height: 35 cm
diagonal: 37 cm

[tex]d^2+h^2=12^2+35^2 \\ \\ =144+1,225=1,369=37^2=l^2[/tex]

Thus, the lateral surface of model 2 meets the base at right angle.

For model 3:

radius: 20 cm, thus, diameter = 2(20) = 40 cm
height: 40 cm
diagonal: 60 cm

 $d^2+h^2=40^2+40^2 \\ \\ =1,600+1,600=3,200\neq60^2=l^2$

Thus, the lateral surface of model 3 does not meets the base at right angle.

For model 4:

radius: 24 cm, thus, diameter = 2(24) = 48 cm
height: 9 cm
diagonal: 30 cm

 $d^2+h^2=48^2+9^2 \\ \\ =2,304+81=2,385\neq30^2=l^2$

Thus, the lateral surface of model 3 does not meets the base at right angle.

Therefore, the model in which the lateral surface meets the base at a right angle is model 2 (option b)

8 0

4 years ago

Read 2 more answers

The graph shows information about Dan’s walk, which statement correctly describes Dan’s walk

GaryK [48]

Answer:

4 playing the game is the most

8 0

3 years ago