Question
Find the two solutions to tan x=-2.55 for 0°≤ x≤ 360°. Give your answers to 1 d.p.
Gauth AI Solution
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Answer
The two solutions are approximately $$-68.2^{\circ}$$ and $$248.2^{\circ}$$
Explanation
- Find the value of x such that $$\tan x=-2.55$$ in the second quadrant by doing $$x=\arctan(-2.55)$$
- Calculate the angle in the second quadrant: $$x \approx -68.2^{\circ}$$
- Find the corresponding angle in the third quadrant: $$180^{\circ} - (-68.2^{\circ})$$
- Calculate the angle in the third quadrant: $$180^{\circ} + 68.2^{\circ} \approx 248.2^{\circ}$$
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