taiwan-gsat 2025 Q5

taiwan-gsat · Other · gsat__math-a 5 marks Quadratic trigonometric equations

Let $0 \leq \theta \leq 2 \pi$. All $\theta$ satisfying $\sin 2 \theta > \sin \theta$ and $\cos 2 \theta > \cos \theta$ can be expressed as $a \pi < \theta < b \pi$, where $a$ and $b$ are real numbers. What is the value of $b - a$?
(1) $\frac { 1 } { 3 }$
(2) $\frac { 1 } { 2 }$
(3) $\frac { 2 } { 3 }$
(4) $\frac { 3 } { 4 }$
(5) 1

Let $0 \leq \theta \leq 2 \pi$. All $\theta$ satisfying $\sin 2 \theta > \sin \theta$ and $\cos 2 \theta > \cos \theta$ can be expressed as $a \pi < \theta < b \pi$, where $a$ and $b$ are real numbers. What is the value of $b - a$?\\
(1) $\frac { 1 } { 3 }$\\
(2) $\frac { 1 } { 2 }$\\
(3) $\frac { 2 } { 3 }$\\
(4) $\frac { 3 } { 4 }$\\
(5) 1

Paper Questions

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