Question 926571
Draw an appropriate triangle to find the exact value of :
 1. csc45°
Draw a 45-45-90 right triangle.
Let the equal sides be "1".
Then the hypotenuse is sqrt(1^2+1^2) = sqrt(2)
Then csc(45) = hyp/opp = sqrt(2)/1 = sqrt(2)
---------------------------------
 2. cot30°
Draw a 30-60-90 right triangle.
Let the side opposite the 30 degree angle be "1"
Then the hypotenuse is "2" and the base is sqrt[2^2-1^2] = sqrt(3)
Then cot(30) adj/opp =  sqrt(3)/1 = sqrt(3)
--------------------------------
 3. sec45°
Use the triangle from #1
sec(45) = hyp/adj = sqrt(2)/1 = sqrt(2)
--------------------------
 4. cot60°
Use the triangle from #2
cot(60) = adj/opp = 1/sqrt(3)
=======================
Cheers,
Stan H.
-----------------------