Additional Concepts
-$\mathrm { r } \cos \left( \theta + \frac { \pi } { 6 } \right) = 1$
A) $\mathrm { y } = \mathrm { x } \sqrt { 3 } - 2 ;$ slope: $\sqrt { 3 } ; y$-intercept: $- 2$
B) $\mathrm { y } = - \mathrm { x } \sqrt { 3 } - 2 ;$ slope: $- \sqrt { 3 } ; \mathrm { y }$-intercept: $- 2$
C) $\mathrm { y } = \mathrm { x } \sqrt { 3 } + 2$; slope: $\sqrt { 3 } ; \mathrm { y }$-intercept: 2
D) $\mathrm { y } = - \mathrm { x } \sqrt { 3 } + 2$; slope: $- \sqrt { 3 }$; $\mathrm { y }$-intercept: 2

Question

Quizplus · Accepted Answer

The equation $\mathrm { r } \cos \left( \theta + \frac { \pi } { 6 } \right) = 1$ can be converted to Cartesian coordinates by using the identity $r\cos\theta = x$ and $r\sin\theta = y$, and the angle sum formula for cosine. After simplification, it results in the equation $y = x\sqrt{3} - 2$, which matches choice A with a slope of $\sqrt{3}$ and a $y$-intercept of $-2$.

Additional Concepts - rcos⁡(θ+π6)=1\mathrm { r } \cos \left( \theta + \frac { \pi } { 6 } \right) = 1rcos(θ+6π​)=1

Additional Concepts
- $\mathrm { r } \cos \left( \theta + \frac { \pi } { 6 } \right) = 1$