Answer:
the answer to 315 / 3 is 105
Subtracting by 1 is the rate of change represented
The slope of the line is: -3/2
Step-by-step explanation:
z
3
=8(cos216
∘
+isin216
∘
)
z^3=2^3(\cos(6^3)^\circ+i\sin(6^3)^\circ)z
3
=2
3
(cos(6
3
)
∘
+isin(6
3
)
∘
)
\implies z=8^{1/3}\left(\cos\left(\dfrac{216+360k}3\right)^\circ+i\sin\left(\dfrac{216+360k}3\right)^\circ\right)⟹z=8
1/3
(cos(
3
216+360k
)
∘
+isin(
3
216+360k
)
∘
)
where k=0,1,2k=0,1,2 . So the third roots are
\begin{gathered}z=\begin{cases}2(\cos72^\circ+i\sin72^\circ)\\2(\cos192^\circ+i\sin192^\circ)\\2(\cos312^\circ+i\sin312^\circ)\end{cases}\end{gathered}
z=
⎩
⎪
⎪
⎨
⎪
⎪
⎧
2(cos72
∘
+isin72
∘
)
2(cos192
∘
+isin192
∘
)
2(cos312
∘
+isin312
∘
)
Question writer: it's customary to keep the degree sign off of the variable names in trig.
sin y = s/8
tan y = s/t
tan y = sin y / cos y
cos y = sin y / tan y
cos y = (s/8) / (s/t) = (s/8) × (t/s) = t/8
Answer: cos y = t/8, third choice