Math  /  Trigonometry

Question[TI - 15 marks] 121-2 1. Solve cos2x2sinxcos2x=3\cos 2 x-2 \sin x-\cos ^{2} x=-3 on the interval x[0,2π]x \in[0,2 \pi]. 12sin2x2sinxcos2x=31-2 \sin ^{2} x-2 \sin x-\cos ^{2} x=-3 12sin2x2sinx(1sin2x)=31-2 \sin ^{2} x-2 \sin x-\left(1-\sin ^{2} x\right)=-3 sin2x2sinx=3-\sin ^{2} x-2 \sin x=3 (sinx+3)(sinx1)=0(\sin x+3)(\sin x-1)=0 sinx=1\therefore \sin x=1 at x=π2x=\frac{\pi}{2} in the sinx=3\sin x=-3 or sinx=1\sin x=1
2. A grandfather clock shows a time of 7070^{\circ} clock. What is the exact radian measure of the angle between the hour hand and the minute hand?

Studdy Solution
The solution to the trigonometric equation cos2x2sinxcos2x=3\cos 2x - 2\sin x - \cos^2 x = -3 in the interval [0,2π][0, 2\pi] is x=π2x = \frac{\pi}{2}.
The angle between the hour and minute hands of a clock at 7 o'clock is 7π6\frac{7\pi}{6} radians.

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