How do you find all values of t in the interval $[0,2pi]$ satisfying the given equation $4cos^2t+4=5$ ?

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Answer 1 · 2016-12-26T15:39:44

$pi/3, (2pi)/3, (4pi)/3, (5pi)/3$

Solve for $cos t$ as follows;

$4 cos^2 t= 5-4=1$

$cos^2 t =1/4$

$cos t= +1/2, -1/2$

For $cos t= +1/2$ , $t$ would lie in Ist and IVth Quadrant. It would be $pi/3$ or $-pi/3= 2pi-pi/3= (5pi)/3$ in the interval $[0,2pi]$ .

For $cos t= -1/2, t$ would lie in IInd and IIIrd Quadrant. It would be $pi-pi/3= (2pi)/3, or pi+pi/3= (4pi)/3$

How do you find all values of t in the interval [0,2pi][0,2pi] satisfying the given equation 4cos^2t+4=54cos^2t+4=5?