SOLUTION: Find all exact solutions on the interval
0 ≤ x < 2𝜋. (Enter your answers as a comma-separated list.)
cot(x) + 7 = 6
Algebra ->
Trigonometry-basics
-> SOLUTION: Find all exact solutions on the interval
0 ≤ x < 2𝜋. (Enter your answers as a comma-separated list.)
cot(x) + 7 = 6
Log On
Use the unit circle to determine the solutions to tan(theta) = -1 are theta = 3𝜋/4 radians and theta = 7𝜋/4 radians.
These angles are in quadrants 2 and 4 respectively.
3𝜋/4 radians = 135 degrees
7𝜋/4 radians = 315 degrees
These two angles are separated by 180 degrees (aka 𝜋 radians), which is half a revolution.
Use a calculator in radian mode to confirm that
tan(3𝜋/4) = -1
tan(7𝜋/4) = -1
I'll let the student check each solution back into the original equation.
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