TRIG HELP! How do I solve the following equation? sin(tan^-1(-5/2))

[Sheeneng]

How do I solve the following equation?
sin(tan^-1(-5/2))
I know that I have to find the angle or radian which gives me the following sinx/cosx that is -5/2 but then I get lost there
Please explain every step

 

[Deleted member 4993]

How do I solve the following equation?
sin(tan^-1(-5/2))
I know that I have to find the angle or radian which gives me the following sinx/cosx that is -5/2 but then I get lost there
Please explain every step

tan(Θ) = a/b

sin(Θ) = ± a/√(a²+b²)

cos(Θ) = ± b/√(a²+b²)

Now continue.....

 

[Sheeneng]

tan(Θ) = a/b

sin(Θ) = ± a/√(a²+b²)

cos(Θ) = ± b/√(a²+b²)

Now continue.....

Thank you! I got -5/sqrt29 .

 

[Deleted member 4993]

Thank you! I got -5/sqrt29 .

How do know you it is negative? The angle Θ could be second quadrant i.e. π/2 < Θ < π