the question in Englih
Hello, I am asking you for 1 task, I have 10 minutes thanks!
we have that
a) cos(x)=-(√10)/10 for x ∈ [pi/2,pi]--------> [90°,180°] I cuadrant
we know that
x=arccos (-(√10)/10)=108.43°
if 180°---------> pi radian
108.43°--------> X
X=108.43/180=0.60pi
the answer part a) is x=0.60pi (108.43°)
b) tan(x)=2 for x ∈ [pi,(3/2)pi]----------> [180°,270°] ------> III quadrant
we know that
x=arctan (2)=63.43°---------> ∉ III quadrant
therefore
x=180°+63.43°=243.43°
if 180°---------> pi radian
243.43°--------> X
X=243.43/180=1.35pi
the answer part b) is x=1.35pi (243.43°)
part c)
x=2alfa
cos(x)=-1/3 for x∈ [(3/2)pi,2pi]----------> [270°,360°]-----> IV quadrant
we know that
x=arccos (-1/3)=109.47°---------> ∉ IV quadrant
therefore
x=109.47°+180°=289.47°
if 180°---------> pi radian
289.47°--------> X
X=289.47°/180°=1.61pi
x=2alfa
alfa=x/2---------> 289.47°/2=144.74°
alfa=1.61pi/2=0.81pi
the answer part c) is alfa=0.81 pi (144.74°)
the answer in Polish
mamy to
a) cos(x)=-(√10)/10 for x ∈ [pi/2,pi]--------> [90°,180°] I cuadrant
wiemy to
x=arccos (-(√10)/10)=108.43°
if 180°---------> pi radian
108.43°--------> X
X=108.43/180=0.60pi
część odpowiedzi a) jest x=0.60pi (108.43°)
b) tan(x)=2 for x ∈ [pi,(3/2)pi]----------> [180°,270°] ------> III quadrant
wiemy to
x=arctan (2)=63.43°---------> ∉ III quadrant
w związku z tym
x=180°+63.43°=243.43°
if 180°---------> pi radian
243.43°--------> X
X=243.43/180=1.35pi
część odpowiedzi b) jest x=1.35pi (243.43°)
c) cos(x)=-1/3
x=2alfa
cos(x)=-1/3 for x∈ [(3/2)pi,2pi]----------> [270°,360°]-----> IV quadrant
wiemy to
x=arccos (-1/3)=109.47°---------> ∉ IV quadrant
w związku z tym
x=109.47°+180°=289.47°
if 180°---------> pi radian
289.47°--------> X
X=289.47°/180°=1.61pi
x=2alfa
alfa=x/2---------> 289.47°/2=144.74°
alfa=1.61pi/2=0.81pi
część odpowiedzi c) jest alfa=0.81 pi (144.74°)
