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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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