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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...

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tylak | Student

t=23.57

or

t=-23.57

giorgiana1976 | Student

We'll verify if the given identity makes sense.

We'll take square root both sides:

sqrt [(sin t)^2] = sqrt(4/25)

sin t = +2/5 or sin t = -2/5

Since the values of the sine function belong to the range [-1 ; 1], the given identity makes sense.

We'll sove the 1st case:

sin t = +2/5

t = (-1)^k*arcsin (2/5) + k*pi

We'll solve the 2nd case:

sin t = -2/5

angle t = (-1)^(k+1)*arcsin (2/5) + k*pi

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