Question

How do you evaluate the sine, cosine, tangent, cosecant, secant, and cotangent of t=7pi/4?

Answer 1

See below.

Explanation:

Switch your calculator to radians.
Press `sin "and then " (7pi/4)` then enter. That's the sine.
Press 1/x. That gives you the cosecant.

Press `cos "and then " (7pi/4)` then enter. That's the cosine.
Press 1/x. That gives you the secant.

Press `tan "and then " (7pi/4)` then enter. That's the tangent.
Press 1/x. That gives you the cotangent.

I hope this helps,
Steve

Answer 2

`t = (7pi)/4 = (- pi/4 + (8pi)/4) = (- pi/4 + 2pi)`
Use trig table and unit circle -->
`sin t = sin (-pi/4) = - sin (pi/4) = - sqrt2/2`
`cos t = cos (-pi/4) = cos (pi/4) = sqrt2/2`
`tan t = sin t/(cos t) = - 1`
`cot t = 1/(tan t) = - 1`
`sec t = 1/(cos t) = 2/sqrt2 = sqrt2`
`csc t = 1/(sin t) = - 2/sqrt2 = - sqrt2`