1. The problem statement, all variables and given/known data
The terminal arm of an angle in standard position passes through (-7,8). Find the radian value of the angle in the interval [0,2∏], to the nearest hundredth.
2. Relevant equations
sinθ = [itex]\frac{y}{r}[/itex]
cosθ = [itex]\frac{x}{r}[/itex]
tanθ = [itex]\frac{y}{x}[/itex]
3. The attempt at a solution
The terminal arm is in quadrant 2, and I found the side lengths to be -7,8, and [itex]\sqrt{113}[/itex] (hypotenuse). When I tried to find the value of θ I get different answers for different ratios.
θ = sin[itex]^{-1}[/itex][itex]\frac{8}{\sqrt{113}}[/itex]
θ = cos[itex]^{-1}[/itex][itex]\frac{-7}{\sqrt{113}}[/itex]
θ = tan[itex]^{-1}[/itex][itex]\frac{8}{-7}[/itex]
The correct one is θ=2.29. Why is this correct and not the others?
The terminal arm of an angle in standard position passes through (-7,8). Find the radian value of the angle in the interval [0,2∏], to the nearest hundredth.
2. Relevant equations
sinθ = [itex]\frac{y}{r}[/itex]
cosθ = [itex]\frac{x}{r}[/itex]
tanθ = [itex]\frac{y}{x}[/itex]
3. The attempt at a solution
The terminal arm is in quadrant 2, and I found the side lengths to be -7,8, and [itex]\sqrt{113}[/itex] (hypotenuse). When I tried to find the value of θ I get different answers for different ratios.
θ = sin[itex]^{-1}[/itex][itex]\frac{8}{\sqrt{113}}[/itex]
= 0.85
θ = cos[itex]^{-1}[/itex][itex]\frac{-7}{\sqrt{113}}[/itex]
= 2.29
θ = tan[itex]^{-1}[/itex][itex]\frac{8}{-7}[/itex]
= -0.85
The correct one is θ=2.29. Why is this correct and not the others?
via Physics Forums RSS Feed http://www.physicsforums.com/showthread.php?t=719639&goto=newpost
0 commentaires:
Enregistrer un commentaire