3.3 Trigonometry

• A right-angled triangle has one angle equal to 90 degrees.
• The hypotenuse is always the longest side in a right-angled triangle.


  True
• The adjacent side is next to the angle we are focusing on, excluding the hypotenuse.
• Match the trigonometric ratio with its definition:

  Sine (sin) ↔️ opposite / hypotenuse

  Cosine (cos) ↔️ adjacent / hypotenuse

  Tangent (tan) ↔️ opposite / adjacent
• Steps to find the length of an unknown side using trigonometric ratios:

  1️⃣ Identify the known angle and side

  2️⃣ Choose the appropriate ratio (sine, cosine, or tangent)

  3️⃣ Set up the equation

  4️⃣ Solve for the unknown side
• To find the length of an unknown side using trigonometric ratios, you must first identify the known angle and side.


  True
• The hypotenuse changes depending on which angle you're considering in a right-angled triangle.

  False
• Cosine (cos) is the ratio of the adjacent side to the hypotenuse.
• In a right-angled triangle with a 30° angle and a hypotenuse of 10 cm, the opposite side is 5 cm.
• Use tangent when you know the opposite and the adjacent
• What is the defining characteristic of a right-angled triangle?

  One 90-degree angle
• The cosine ratio is the ratio of the adjacent side to the hypotenuse
• To find an unknown angle using trigonometric ratios, you use the inverse trigonometric functions.


  True
• To find an unknown angle, the appropriate ratio for opposite and hypotenuse is sine
• Which trigonometric ratio is used when you know the adjacent and need to find the hypotenuse?

  Cosine
• When solving for the opposite side using sine, the equation is sin(θ) = opposite / hypotenuse
• What are three key applications of trigonometric ratios in the real world?

  Navigation, surveying, engineering
• What do sailors and pilots use trigonometry for in navigation?

  Calculate distances and bearings
• In a right-angled triangle with a 30° angle and a hypotenuse of 10 cm, the opposite side is 5 cm.


  True
• The hypotenuse remains the same, but the opposite and adjacent sides change depending on the angle
• Steps to find an unknown side using trigonometric ratios

  1️⃣ Identify the known angle and side.

  2️⃣ Choose the appropriate ratio.

  3️⃣ Set up the equation.

  4️⃣ Solve for the unknown side.
• What is the first step in finding an unknown angle using trigonometric ratios?

  Identify the known sides
• To set up the equation, the inverse trigonometric function is applied to the ratio of the sides
• Steps to solve problems involving trigonometry

  1️⃣ Identify the known sides and angles

  2️⃣ Choose the appropriate trigonometric ratio

  3️⃣ Set up the equation

  4️⃣ Solve the equation
• If the opposite side is 4 cm and the hypotenuse is 8 cm, the angle is 30°.


  True
• Trigonometric ratios are used to solve practical problems involving angles and lengths in right-angled triangles.

  True
• Trigonometric ratios relate the sides of a right-angled triangle to its angles.


  True
• Use sine when you know the opposite
• Steps to find an unknown side using trigonometric ratios

  1️⃣ Identify the known angle and side.

  2️⃣ Choose the appropriate ratio.

  3️⃣ Set up the equation.

  4️⃣ Solve for the unknown side.
• Match the side of a right-angled triangle with its definition:

  Hypotenuse ↔️ Longest side opposite the right angle

  Opposite ↔️ Side across from the angle

  Adjacent ↔️ Side next to the angle
• Trigonometric ratios relate the sides of a right-angled triangle to its angles.

  True
• If the opposite side is 4 cm and the hypotenuse is 8 cm, the angle θ is 30° using the inverse sine function.sin⁻¹
• The inverse trigonometric functions are sin⁻¹, cos⁻¹, and tan⁻¹.


  True
• What tool is used to solve for the angle after setting up the equation?

  Calculator
• To solve problems involving trigonometry, the first step is to identify the known sides and angles.

  True
• What is the final step in solving a trigonometry problem?

  Solve the equation
• Match the application with the trigonometric ratio used:

  Navigation ↔️ Sine, Cosine, Tangent

  Surveying ↔️ Cosine, Tangent

  Engineering ↔️ Sine, Tangent