Trigonometry
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선생님을 위해: Trigonometry(Maths [CIE], Core)을(를) 위한 바로 쓸 수 있는 수업 슬라이드, 복습 노트, 다이어그램 — 수업에 사용하거나, 학생들이 실시간 게임으로 즐기는 인터랙티브 클래스 활동으로 진행하세요.
수업 노트
Trigonometry Basics
- Trigonometry is the mathematics of angles in triangles, studying relationships between side lengths and angles.
- The three trigonometric functions are sine, cosine, and tangent (sin, cos, tan).
- These functions are ratios of side lengths in right-angled triangles.
- SOHCAHTOA is a mnemonic to remember the ratios: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
- Trigonometry (like Pythagoras) can only be used in right-angled triangles.
- Ensure your calculator is set to degrees (D or Deg on screen).
Labelling Sides of a Right-Angled Triangle
- Label the sides relative to a chosen angle θ: Hypotenuse (H) – longest side, opposite the right angle.
- Opposite (O) – side directly opposite angle θ.
- Adjacent (A) – side next to angle θ (not the hypotenuse).
- H is always the same; O and A change depending on which angle is θ.
Labelling a right-angled triangle
Finding Missing Lengths Using SOHCAHTOA
- Step 1: Label the sides as H, O, A relative to the given angle.
- Step 2: Identify which ratio to use: given two sides, find the two letters in SOHCAHTOA (e.g., O and A → tan).
- Step 3: Substitute values into the formula: e.g., tan(θ) = O/A.
- Step 4: Rearrange to solve for the unknown side (multiply or divide).
- Step 5: Type into calculator and round to 3 significant figures unless otherwise stated.
- Example: If tan(43°) = x/9, then x = 9 × tan(43°) = 8.39 cm (3 s.f.).
Finding a length: worked example
Finding Missing Angles Using SOHCAHTOA
- Step 1: Label sides as H, O, A relative to the unknown angle.
- Step 2: Identify the ratio using the two given side letters (e.g., A and H → cos).
- Step 3: Write the ratio as a fraction: cos(θ) = A/H.
- Step 4: Use the inverse trigonometric function (sin⁻¹, cos⁻¹, tan⁻¹) – press SHIFT on calculator.
- Step 5: Calculate and round to 1 decimal place unless otherwise stated.
- Example: If cos(y) = 8/23, then y = cos⁻¹(8/23) = 69.6° (1 d.p.).
Finding an angle: worked example
Common Exam Tips
- Always label the triangle first before applying SOHCAHTOA.
- Write down the ratio you are using to avoid mistakes.
- For lengths, round to 3 significant figures; for angles, round to 1 decimal place.
- Check your calculator mode: it must be in degrees.
- SOHCAHTOA only works in right-angled triangles – do not use it for non-right triangles.
슬라이드
연습 문제
무료 미리 보기 — 59개 중 8개 문제. 가입하면 전부 볼 수 있어요.
1.In a right-angled triangle, which side is the hypotenuse?
Easy- AThe side opposite the right angle
- BThe side opposite the given angle
- CThe side adjacent to the given angle
- DThe shortest side
2.What does SOHCAHTOA stand for?
Easy- ASin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent
- BSin = Adjacent/Hypotenuse, Cos = Opposite/Hypotenuse, Tan = Adjacent/Opposite
- CSin = Hypotenuse/Opposite, Cos = Hypotenuse/Adjacent, Tan = Adjacent/Opposite
- DSin = Opposite/Adjacent, Cos = Adjacent/Hypotenuse, Tan = Hypotenuse/Opposite
3.If tan θ = opposite/adjacent, which sides are used for tan?
Easy- AOpposite and adjacent
- BOpposite and hypotenuse
- CAdjacent and hypotenuse
- DHypotenuse and opposite
4.In a right-angled triangle, the adjacent side is 8 cm and the hypotenuse is 17 cm. What is cos θ?
Easy- A8/17
- B17/8
- C15/17
- D8/15
5.In a right-angled triangle, the adjacent side is 9 cm and the opposite side is 12 cm. Find tan θ.
Easy- A1.333
- B0.750
- C0.800
- D1.250
6.A right-angled triangle has opposite side 5 cm and hypotenuse 13 cm. Find the adjacent side.
Easy- A12 cm
- B8 cm
- C10 cm
- D9 cm
7.In a right-angled triangle, the angle is 60° and the opposite side is 10 cm. Find the hypotenuse.
Medium- A11.55 cm
- B8.66 cm
- C5.77 cm
- D20.0 cm
8.A right-angled triangle has adjacent side 7 cm and hypotenuse 25 cm. Find the angle θ.
Medium- A73.7°
- B16.3°
- C45.0°
- D30.0°
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