Math  /  Trigonometry

Question5. Determine exact values of θ\theta if 0θ2π0 \leq \theta \leq 2 \pi given that tanθ=3\tan \theta=-\sqrt{3} [5 marks]

Studdy Solution
Calculate the exact values of θ\theta in the second and fourth quadrants:
In the second quadrant, the angle is:
θ=πα=ππ3=2π3 \theta = \pi - \alpha = \pi - \frac{\pi}{3} = \frac{2\pi}{3}
In the fourth quadrant, the angle is:
θ=2πα=2ππ3=5π3 \theta = 2\pi - \alpha = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}
The exact values of θ\theta are:
2π3,5π3 \boxed{\frac{2\pi}{3}, \frac{5\pi}{3}}

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