Posted by lola on Monday, January 16, 2012 at 7:11pm.
The best way to solve these problems is to draw a unit circle (radius = 1), and calculate these ratios from the definitions (cosine = adjacent / hypotenuse, etc.)
The first three can be solved easily this way. The last one,
csc(45°)=1/sin(45°)
Knowing that sin(45)=cos(45), and
sin²(45)+cos²(45)=1, we solve for sin(45)=(√2)/2, so
csc(45)=2/√2 = √2.
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