Answer:
![\sin 105^{\circ} = \frac{\sqrt{6}+\sqrt {2}}{4}](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B6%7D%2B%5Csqrt%20%7B2%7D%7D%7B4%7D)
Step-by-step explanation:
We can use the following trigonometrical identity:
(1)
Where
,
are angles, measured in sexagesimal degrees.
If we know that
and
, then the value of the given function is:
![\sin 105^{\circ} = \sin 135^{\circ}\cdot \cos 30^{\circ} - \cos 135^{\circ}\cdot \sin 30^{\circ}](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Csin%20135%5E%7B%5Ccirc%7D%5Ccdot%20%5Ccos%2030%5E%7B%5Ccirc%7D%20-%20%5Ccos%20135%5E%7B%5Ccirc%7D%5Ccdot%20%5Csin%2030%5E%7B%5Ccirc%7D)
![\sin 105^{\circ} = \left(\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{\sqrt{3}}{2}\right)-\left(-\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{1}{2}\right)](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Cleft%28%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5Cright%29-%5Cleft%28-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29)
![\sin 105^{\circ} = \frac{\sqrt{6}}{4}+\frac{\sqrt{2}}{4}](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B4%7D%2B%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B4%7D)
![\sin 105^{\circ} = \sqrt{\frac{6}{16} }+\sqrt{\frac{2}{16} }](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B6%7D%7B16%7D%20%7D%2B%5Csqrt%7B%5Cfrac%7B2%7D%7B16%7D%20%7D)
![\sin 105^{\circ} = \sqrt{\frac{3}{8} }+\sqrt{\frac{1}{8} }](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B3%7D%7B8%7D%20%7D%2B%5Csqrt%7B%5Cfrac%7B1%7D%7B8%7D%20%7D)
![\sin 105^{\circ} = \frac{\sqrt{3}+1}{2\cdot \sqrt{2}}](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%2B1%7D%7B2%5Ccdot%20%5Csqrt%7B2%7D%7D)
![\sin 105^{\circ} = \frac{\sqrt{6}+\sqrt {2}}{4}](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B6%7D%2B%5Csqrt%20%7B2%7D%7D%7B4%7D)
Answer:
It's A.
Step-by-step explanation:
this is a right angled triangle with the 2 legs = (a - 0) and (b - 0) - a and b.
So, by Pythagoras Theorem the hypotenuse = √(a^2 + b^2).
<h2>
Answer: (−∞,∞)</h2>
Step-by-step explanation:
Answer:
-7/2
Step-by-step explanation:
the slope is the number multiplying x, so in this case it would be -7/2
Remember the formula is y=mx+b where m is slope and b is the y-intercept.