Question

Approximate the solutions to the following equation on the interval ​[0,2​π). Round your answer to four decimal places.

tanθ=-10

Answer 1

θ ≈ {1.6705, 4.8121}

Explanation:

You want the solutions to the equation tan(θ) = -10.

Solution

A graphing calculator or scientific calculator can tell you these values.

A scientific calculator will tell you the inverse tangent of -10 is a negative number. To put the value into the desired range, multiples of pi must be added.

tan(θ) = -10

θ = arctan(-10) ≈ -1.471128 +nπ

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Additional comment

The angle units used here are radians, since the desired interval is expressed in radians. (Not [0, 360°).)