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Proof of complementary angle identities
  • Understanding the concept of complementary angles (two angles adding up to 90°).
  • Learning the complementary angle identities in trigonometry:
    • sin(π/2 - θ) = cos θ
    • cos(π/2 - θ) = sin θ
    • tan(π/2 - θ) = 1 / tan θ
  • Using a circle and coordinates to visualise and prove trigonometric identities.
  • How to derive trigonometric identities from the definitions of sine, cosine, and tangent.
  • Recognising the relationship between the coordinates of points corresponding to angles θ and (π/2 - θ).
  • Developing skills to prove trigonometric identities instead of memorising them.
Complementary angle identities
  • sin(π/2 − θ) = cos θ
  • cos(π/2 − θ) = sin θ
  • tan(π/2 − θ) = 1 / tan θ (tan θ ≠ 0)
Degree measure and radian measure
  • Difference between degree measure and radian measure
  • What radian measure is
  • How to convert between degree measures and radian measure
Supplementary angle identities
  • How to use \sin{(\pi - \theta)} = \sin{\theta}
  • How to use \cos{(\pi - \theta)} = -\cos{\theta}
  • How to use \tan{(\pi - \theta)} = -\tan{\theta}
  • When to use the supplementary angle identities
Proof of supplementary angle identities in trigonometry
  • Proof of sin (π - θ) = sinθ
  • Proof of cos (π - θ) = - cosθ
  • Proof of tan(π - θ) = - tanθ
三角関数の補角の公式 使い方
  • \sin{(\pi - \theta)} = \sin{\theta}の使い方
  • \cos{(\pi - \theta)} = -\cos{\theta}の使い方
  • \tan{(\pi - \theta)} = -\tan{\theta}の使い方
  • 補角の公式をいつ使うのか
Definition of trigonometric functions title
  • Definition of Trigonometric Functions
  • Relationship between Coordinates of Points on the Circle and the Radius
  • How to Calculate Values of Trigonometric Functions Using the Definition
trigonometric functions are independent of the radius title
  • The Reason Why Trigonometric Functions are Independent of Radii
余角の公式
  • 余角の公式の解説と練習
  • \sin{\left(\frac{\pi}{2} - \theta \right)} = \cos{\theta}の解説
  • \cos{\left(\frac{\pi}{2} - \theta \right)} = \sin{\theta}
  • \tan{\left(\frac{\pi}{2} - \theta \right)} = \frac{1}{\tan{\theta}}の解説
三角関数の公式 負の角度
  • \sin{(-\theta)} = -\sin{\theta}の解説と練習
  • \cos{(-\theta)} = \cos{\theta}の解説と練習
  • \tan{(-\theta)} = -\tan{\theta}の解説と練習