+1094 secant: the reciprocal of a cosine
This just goes to say that the cosine of theta is 1/sqrt(5)
But...how does this help...at all? Well, you could just go and find the sin(arccos(1/sqrt(5)) and waste a lot of time trying, or you could use the fact that:
sin(theta)^2 + cos(theta)^2 = 1
With what we know, we can say this:
sin(theta)^2 + (1/sqrt(5))^2 = 1
sin(theta)^2 + 1/5 = 1
sin(theta)^2 = 4/5
sin(theta) = 2/sqrt(5)
Edit: oops, forgot to rationalize the denominator!
Multiply top and bottom by sqrt(5):
2sqrt(5)/5
:)
