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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t=23.57
or
t=-23.57
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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