Confused with maths question involving the "t formula"

[ConfusedWithMaths]

I have let t = tan a for the first 3 parts (a, b and c), but I am confused with how I should do part d.

 

[lev888]

Use the inverse of the first formula.

 

[jonah2.0]

Beer soaked ramblings follow.

View attachment 28403
I have let t = tan a for the first 3 parts (a, b and c), but I am confused with how I should do part d.

[imath]\tan\alpha=-\frac{1}{3}[/imath] and [imath]\frac{\pi}{2}<\alpha<\pi[/imath] [imath]\implies[/imath] [imath]a=1[/imath], [imath]b=-3[/imath], & [imath]c=\sqrt{a^2+b^2}[/imath].

Just plug and chug using the 1st three of the Double-Angle Identities and the 3rd of the Half-Angle Identities.

 

[ConfusedWithMaths]

Beer soaked ramblings follow.

[imath]\tan\alpha=-\frac{1}{3}[/imath] and [imath]\frac{\pi}{2}<\alpha<\pi[/imath] [imath]\implies[/imath] [imath]a=1[/imath], [imath]b=-3[/imath], & [imath]c=\sqrt{a^2+b^2}[/imath].

Just plug and chug using the 1st three of the Double-Angle Identities and the 3rd of the Half-Angle Identities.
View attachment 28406

Thank you very much!

 

[ConfusedWithMaths]

Use the inverse of the first formula.

Thank you!