#1**+1 **

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**

**:)**

ilorty Aug 28, 2020