SOLUTION: If 25 cosx-3sinx =0 find tanx and cot

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Question 1012039: If 25 cosx-3sinx =0 find tanx and cot
Found 2 solutions by ValorousDawn, ikleyn:
Answer by ValorousDawn(53) About Me  (Show Source):
You can put this solution on YOUR website!
We have 25cos%28x%29-3sin%28x%29=0
Divide across by cos(x). %2825-cos%28x%29%29%2Fcos%28x%29-%283sin%28x%29%29%2Fcos%28x%29=0%2Fcos%28x%29, with the fact that cos(x) cannot be 0, as we cannot divide by 0.
Rearrange, and simplify to get 25-3sin%28x%29%2Fcos%28x%29=0
Recall that tan%28x%29=sin%28x%29%2Fcos%28x%29 to get 25-3tan%28x%29=0
Isolate tan(x) by adding 3tan(x) to both sides and then dividing by 3. tan%28x%29=25%2F3
Recall that cot%28x%29=1%2Ftan%28x%29. Substitute this in to get cot%28x%29=3%2F25
However, these are only the terminal angles, you must include multiple revolutions in your answer.
tan%28x%29=25%2F3%2B2npi
cot%28x%29=3%2F25%2B2npi

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
The previous tutor found that
tan%28x%29 = 25%2F3.

It implies that x = arctan%2825%2F3%29+%2B+k%2Api, k = 0, +/-1, +/2, . . .

The Tangent function is periodic with the period pi.