Observe that
![\sin\left(\dfrac\pi6-v\right)=\sin\dfrac\pi6\cos v-\cos\dfrac\pi6\sin v=\dfrac12\cos v-\dfrac{\sqrt3}2\sin v](https://tex.z-dn.net/?f=%5Csin%5Cleft%28%5Cdfrac%5Cpi6-v%5Cright%29%3D%5Csin%5Cdfrac%5Cpi6%5Ccos%20v-%5Ccos%5Cdfrac%5Cpi6%5Csin%20v%3D%5Cdfrac12%5Ccos%20v-%5Cdfrac%7B%5Csqrt3%7D2%5Csin%20v)
In the original equation, divide both sides by
:
![-\sqrt3\sin v+\cos v=\sqrt3\implies\dfrac12\cos v-\dfrac{\sqrt3}2\sin v=\dfrac{\sqrt3}2](https://tex.z-dn.net/?f=-%5Csqrt3%5Csin%20v%2B%5Ccos%20v%3D%5Csqrt3%5Cimplies%5Cdfrac12%5Ccos%20v-%5Cdfrac%7B%5Csqrt3%7D2%5Csin%20v%3D%5Cdfrac%7B%5Csqrt3%7D2)
![\implies\sin\left(\dfrac\pi6-v\right)=\dfrac{\sqrt3}2](https://tex.z-dn.net/?f=%5Cimplies%5Csin%5Cleft%28%5Cdfrac%5Cpi6-v%5Cright%29%3D%5Cdfrac%7B%5Csqrt3%7D2)
Next,
![\sin x=\dfrac{\sqrt3}2\implies x=\dfrac\pi3+2n\pi,x=\dfrac{2\pi}3+2n\pi](https://tex.z-dn.net/?f=%5Csin%20x%3D%5Cdfrac%7B%5Csqrt3%7D2%5Cimplies%20x%3D%5Cdfrac%5Cpi3%2B2n%5Cpi%2Cx%3D%5Cdfrac%7B2%5Cpi%7D3%2B2n%5Cpi)
where
is any integer. Then
![\sin\left(\dfrac\pi6-v\right)\implies v=-\dfrac\pi6-2n\pi,v=-\dfrac\pi2-2n\pi](https://tex.z-dn.net/?f=%5Csin%5Cleft%28%5Cdfrac%5Cpi6-v%5Cright%29%5Cimplies%20v%3D-%5Cdfrac%5Cpi6-2n%5Cpi%2Cv%3D-%5Cdfrac%5Cpi2-2n%5Cpi)
Fix
to ensure
, so that
![v=-\dfrac\pi6,v=-\dfrac\pi2](https://tex.z-dn.net/?f=v%3D-%5Cdfrac%5Cpi6%2Cv%3D-%5Cdfrac%5Cpi2)
if you do not have a Unit Circle, this is a great time to get one, you can find many online just do a quick search for "unit circle".
Check the picture below.
Answer:
D
Step-by-step explanation:
10/7 = 1.4285
9/y = 1.4285
Multiply both sides by y.
9 = 1.4285y
Divide both sides by y.
6.3 = y
When a quadrilateral is inscribed in a circle, the opposite angles are supplementary.
x + 2 + 3x + 6 = 180
4x + 8 = 180
4x = 172
x = 43
Now solve for A
3(43) + 6 = A
129 + 6 = A
135 = A
The measure of angle A is 135 degrees.
Hope this helps =)
Answer:
f(1) = 7
f(2) = 18
f(3) = 31
f(4) = 46
f(5) = 63
f(6) = 82
f(7) = 103
f(8) = 126
f(9) = 151
f(10) = 178
Step-by-step explanation:
f(1) = (-1)^2+8(1)-2 = 7
Continue plugging in values...