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Find the value of each of the six trigonometric functions (if it is defined) at the given real number t. Use your answers to complete the table. (If an answer is undefined, enter UNDEFINED.)t = 𝜋2t sin(t) cos(t) tan(t) csc(t) sec(t) cot(t)𝜋2

Question

Find the value of each of the six trigonometric functions (if it is defined) at the given real number t. Use your answers to complete the table. (If an answer is undefined, enter UNDEFINED.)t = 𝜋2t sin(t) cos(t) tan(t) csc(t) sec(t) cot(t)𝜋2

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Solution

t = 𝜋/2

sin(t) = sin(𝜋/2) = 1

cos(t) = cos(𝜋/2) = 0

tan(t) = sin(t)/cos(t) = 1/0 = UNDEFINED

csc(t) = 1/sin(t) = 1/1 = 1

sec(t) = 1/cos(t) = 1/0 = UNDEFINED

cot(t) = cos(t)/sin(t) = 0/1 = 0

So, the table will look like this:

t sin(t) cos(t) tan(t) csc(t) sec(t) cot(t) 𝜋/2 1 0 UNDEFINED 1 UNDEFINED 0

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