What is the value of sec(t), if tan(t) = 1/3?

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Given tan(t) = 1/3.

Recall the identity: 1 + tan^2(t) = sec^2(t).

Step 1: Calculate tan^2(t) = (1/3)^2 = 1/9.

Step 2: Use the identity:    
sec^2(t) = 1 + 1/9 = 10/9.

Step 3: Take square root on both sides:  
sec(t) = √(10/9) = (√10)/3.

Therefore, the value of sec(t) is (√10)/3.

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