Solve tan2𝑥=1 in the interval 0∘<𝑥<360∘Give your solution(s) correct to 2 decimal places where appropriate.
Question
Solve tan2𝑥=1 in the interval 0∘<𝑥<360∘Give your solution(s) correct to 2 decimal places where appropriate.
Solution
The equation tan^2(x) = 1 can be rewritten as tan(x) = ±1.
The tangent function has a period of 180°, so we only need to find the solutions in the interval 0° < x < 180° and then add or subtract multiples of 180° to find the rest of the solutions in the given interval.
In the interval 0° < x < 180°, tan(x) = 1 at x = 45° and tan(x) = -1 at x = 135°.
So, the solutions to the equation in the interval 0° < x < 360° are x = 45°, 135°, 45° + 180° = 225°, and 135° + 180° = 315°.
Therefore, the solutions to the equation tan^2(x) = 1 in the interval 0° < x < 360° are x = 45°, 135°, 225°, and 315°.
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