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Determine the angle t from the identity sin^2t=4/25 .

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You mean determine t from the equation (sin t)^2 = 4/25

(sin t)^2 = 4/25

=> sin t = 2/5 and sin t = -2/5

sin t = 2/5

=> t = arc sin (2/5)

=> t = 23.57 degrees

sin t = -2/5

=> t = arc sin (-2/5)

=> t = -23.57 degrees

As sine is periodic, there are an infinite solutions for t.

The angle t is 23.57 + n*360 degrees and -23.57 + n*360 degrees.

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