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How do you find the exact value of #arctan 1#?

1 Answer
Jul 13, 2017

Answer:

#arctan 1 = pi/4#

Explanation:

Based on the definition of #arctan#, you know that #tan theta = 1#; therefore, #arctan 1 = theta#.

The only values of #theta# that make the equation #tan theta = 1# true are #pi/4# and #(5pi)/4#.

However, we must consider the range of the #arctan# function, which is #(-pi/2, pi/2)#.

Only #pi/4# falls into this interval. Thus, #arctan 1 = pi/4#.