Question 950272: Solve the equation for t on the interval [0,2π) 4 cos t - 4 sin t = 4
Found 2 solutions by lwsshak3, ikleyn:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Solve the equation for t on the interval [0,2π)
4 cos t - 4 sin t = 4
cos t-sin t=1
cos t-1=sin t
cos^2(t)-2cos t+1=sin^2(t)
cos^2(t)-2cos t+1=1-cos^2(t)
2cos^2(t)-2cos t=0
cos^2(t)-cos t=0
cos t(cos t-1)=0
cos t=0
t=π/2, 3π/2
or
cos t-1=0
cos t=1
t=0
Answer by ikleyn(53937)  (Show Source):
You can put this solution on YOUR website! .
Solve the equation for t on the interval [0,2π) 4 cos t - 4 sin t = 4
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@lwsshar3 in his post gives 3 (three) possible answers t = 0, π/2, and 3π/2, without checking.
This answer is INCORRECT.
Since both sides of the equation were squared on the way, the check is needed to test
if the founded possible solutions really satisfy the original equation.
The test shows that t = π/2 does not satisfy the original equation.
Therefore, the true solutions are t = 0, 3π/2, only. ANSWER
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