Questions

• Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

  \(2 + 7i + 5i^2 + 6i^3\) 的虛部是什麼？

  2024

• Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

  計算表達式 \(\frac{3i^{17} + 4i^{18} + 5i^{19} + 6i^{20} + 7i^{21}}{1 + i}\) 的實部。

  2024

• Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

  設 \( x = \frac{5}{b + i} \) 且 \( y = \frac{5}{b - i} \)，其中 \( b \) 為實數。下列哪些必定為真？I. \( xy \) 是一個實數。II. \( x \) 與 \( y \) 的虛部之和為 0。III. \( \frac{1}{x} \) 的實部等於 \( \frac{1}{y} \) 的實部。

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• Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

  設 \( p = \frac{8}{d + i} \) 且 \( q = \frac{8}{d - i} \)，其中 \( d \) 為實數。下列哪些必定為真？I. \( pq \) 是一個有理數。II. \( ip + 2 \) 與 \( iq + 2 \) 的實部相同。III. \( \frac{1}{p} \) 的實部等於 \( \frac{1}{q} \) 的實部。

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• Permutations and Combinations Understand the concept and notation of combination Solve problems on the combination of distinct objects without repetition

  一個閱讀學會有15名女性和10名男性。如果要從該學會中選出6人組成委員會來組織一個文學活動，且委員會必須至少包括兩名女性，那麼可以組成多少個不同的委員會？

  2024

• Trigonometric Ratios and Using Trigonometry understand the sine, cosine and tangent ratios for angles between 0° to 90°

  \(\sin^{2}(2^\circ)+\sin^{2}(4^\circ)+\sin^{2}(6^\circ)+ ... +\sin^{2}(84^\circ)+\sin^{2}(86^\circ)+\sin^{2}(88^\circ)+\sin^{2}(90^\circ) = \)

  2024

• Trigonometric Ratios and Using Trigonometry explore the exact value of trigonometric ratios on special angles 30°, 45°, 60°

  \(\cos^{2}(1^\circ)+\cos^{2}(3^\circ)+\cos^{2}(5^\circ)+ ... +\cos^{2}(85^\circ)+\cos^{2}(87^\circ)+\cos^{2}(89^\circ) = \)

  2024

• More About Trigonometry Solve the trigonometric equations a sin θ = b, a cos θ = b, a tan θ = b (0° to 360°) and other equations

  對於 \(0^{\circ} \leq \theta < 360^{\circ}\)，方程式 \(2 \cos^2 \theta + \cos \theta - 1 = 0\) 有幾個根？

  2024

• More About Trigonometry Solve the trigonometric equations a sin θ = b, a cos θ = b, a tan θ = b (0° to 360°) and other equations

  對於 \(0^{\circ} \leq \theta \leq 360^{\circ}\)，方程式 \(4 \cos^2 \theta - 3 \sin \theta - 1 = 0\) 有幾個根？

  2024

• More About Trigonometry Solve the trigonometric equations a sin θ = b, a cos θ = b, a tan θ = b (0° to 360°) and other equations

  對於\(0^{\circ} \leq \theta \leq 360^{\circ}\)，方程式\(\cos \theta(2\tan \theta - 1) = 0\)有多少個根？

  2024