Answer:
sinβ = 15/17
General Formulas and Concepts:
<u>Math</u>
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] sinθ = opposite over hypotenuse
Step-by-step explanation:
<u>Step 1: Define</u>
Angle θ = β
Opposite Leg = 15
Hypotenuse Leg = 17
<u>Step 2: Find</u>
- Substitute in variables [sine]: sinβ = 15/17
From the double-angle identity,
![cos2x=2*sinx*cosx](https://tex.z-dn.net/?f=cos2x%3D2%2Asinx%2Acosx)
we can rewritte our given equation as:
![4sinxcosx-2cosx=0](https://tex.z-dn.net/?f=4sinxcosx-2cosx%3D0)
By factoring 2cosx on the left hand side, we have
![2cosx(2sinx-1)=0](https://tex.z-dn.net/?f=2cosx%282sinx-1%29%3D0)
This equation has 2 solutions when
![\begin{gathered} cosx=0\text{ ...\lparen A\rparen} \\ and \\ 2sinx-1=0\text{ ...\lparen B\rparen} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20cosx%3D0%5Ctext%7B%20...%5Clparen%20A%5Crparen%7D%20%5C%5C%20and%20%5C%5C%202sinx-1%3D0%5Ctext%7B%20...%5Clparen%20B%5Crparen%7D%20%5Cend%7Bgathered%7D)
From equation (A), we obtain
![x=\frac{\pi}{2}\text{ or }\frac{3\pi}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cpi%7D%7B2%7D%5Ctext%7B%20or%20%7D%5Cfrac%7B3%5Cpi%7D%7B2%7D)
and from equation (B), we have
![\begin{gathered} sinx=\frac{1}{2} \\ which\text{ gives} \\ x=\frac{\pi}{6}\text{ or }\frac{5\pi}{6} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20sinx%3D%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20which%5Ctext%7B%20gives%7D%20%5C%5C%20x%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%5Ctext%7B%20or%20%7D%5Cfrac%7B5%5Cpi%7D%7B6%7D%20%5Cend%7Bgathered%7D)
On the other hand, we can find one more solution from the original equation by substituting x=0, that is,
![\begin{gathered} 2ccos(2\times0)-2cos0=0 \\ which\text{ gives} \\ 2\times1-2\times1=0 \\ so\text{ 0=0} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202ccos%282%5Ctimes0%29-2cos0%3D0%20%5C%5C%20which%5Ctext%7B%20gives%7D%20%5C%5C%202%5Ctimes1-2%5Ctimes1%3D0%20%5C%5C%20so%5Ctext%7B%200%3D0%7D%20%5Cend%7Bgathered%7D)
then, x=0 is another solution. In summary, we have obtained the following solutions:
![\begin{gathered} x=0 \\ x=\frac{\pi}{2}\text{or}\frac{3\pi}{2}\text{ and } \\ x=\frac{\pi}{6}\text{or}\frac{5\pi}{6} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D0%20%5C%5C%20x%3D%5Cfrac%7B%5Cpi%7D%7B2%7D%5Ctext%7Bor%7D%5Cfrac%7B3%5Cpi%7D%7B2%7D%5Ctext%7B%20and%20%7D%20%5C%5C%20x%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%5Ctext%7Bor%7D%5Cfrac%7B5%5Cpi%7D%7B6%7D%20%5Cend%7Bgathered%7D)
However, the intersection of the last set is empty. So the unique solution is x=0 as we can corroborate on the following picture:
Therefore, the solution set is: {0}
Answer:
false
Step-by-step explanation:
Answer:
Each pendant cost $3.30
Step-by-step explanation:
You would subtract $13.20 from $26.20 and get $13.20. You take $13.20 and divide it by 4. You would get $3.30.