14.2.3 Applying trigonometry in physics

• The sine of an angle in a right-angled triangle is defined as the opposite side divided by the hypotenuse
• To resolve a force vector of 50 N acting at 30° to the horizontal, the horizontal component is calculated using cosine
• If a right-angled triangle has sides of 3 cm and 4 cm, the hypotenuse is equal to 5
• When resolving a force vector of 50 N at 30°, the horizontal component is approximately 43.3 N
• A right-angled triangle with sides 3 cm and 4 cm has a hypotenuse of 5 cm
• When resolving a force vector of 50 N at 30°, the vertical component is 25 N
• What are the three primary trigonometric ratios?

  Sine, cosine, tangent
• What does the Pythagorean theorem state?

  $a^{2} +$$b^{2} =$$c^{2}$
• What is a right-angled triangle?

  A triangle with a 90° angle
• Understanding common scenarios helps identify when to apply trigonometry in physics problems.


  True
• Using sine is correct for finding the vertical component of a vector.


  True
• Trigonometry is essential for resolving vectors into their components.


  True
• Trigonometry is crucial for analyzing projectile motion by resolving the initial velocity vector into its components.


  True
• Match the trigonometric ratio with its corresponding wave property:

  Sine ↔️ Amplitude

  Cosine ↔️ Phase

  Tangent ↔️ Wavelength
• What is the equation for the tangent ratio?

  `tan θ = opposite / adjacent`
• Right-angled triangles have one angle that measures 90 degrees
• Trigonometry is crucial in physics for resolving vectors
• Match the scenario with its application of trigonometry:

  Forces at angles ↔️ Resolving force vectors

  Velocity components ↔️ Breaking down velocities

  Distances and angles ↔️ Geometric optics
• Match the trigonometric ratio with its definition and equation:

  Sine ↔️ Opposite / Hypotenuse, sin θ = opposite / hypotenuse

  Cosine ↔️ Adjacent / Hypotenuse, cos θ = adjacent / hypotenuse

  Tangent ↔️ Opposite / Adjacent, tan θ = opposite / adjacent
• To resolve a vector, first identify the vector and its angle
• Match the trigonometric ratio with the wave property it describes:

  Sine ↔️ Amplitude

  Cosine ↔️ Phase

  Tangent ↔️ Wavelength
• The Pythagorean identity can be used to simplify trigonometric expressions.

  True
• The cosine of an angle is the adjacent side divided by the hypotenuse.

  True
• The Pythagorean theorem states that in a right-angled triangle, $a^{2} +$$b^{2} =$$c^{2}$.


  True
• Why is trigonometry essential in physics?

  Resolving vector quantities
• The Pythagorean theorem applies only to right-angled triangles.

  True
• Right-angled triangles have one 90-degree angle.

  True
• The Pythagorean theorem is crucial for understanding the properties of right-angled triangles.


  True
• The sine of an angle is defined as the opposite side divided by the hypotenuse.
• If the sides of a right-angled triangle are 3 cm and 4 cm, the hypotenuse is 5 cm.
• Match the trigonometric ratio with its equation:

  Sine ↔️ $\sin \theta =$$\frac{\text{opposite}}{\text{hypotenuse}}$

  Cosine ↔️ $\cos \theta =$$\frac{\text{adjacent}}{\text{hypotenuse}}$

  Tangent ↔️ $\tan \theta =$$\frac{\text{opposite}}{\text{adjacent}}$
• To find the horizontal component of a vector, you multiply its magnitude by the cosine of the angle.
• What is the horizontal component of a 50 N force acting at 30° to the horizontal?

  43.3 N
• Match the trigonometric ratio with its definition:

  Sine ↔️ Opposite / Hypotenuse

  Cosine ↔️ Adjacent / Hypotenuse

  Tangent ↔️ Opposite / Adjacent
• Which trigonometric ratio is used to describe the amplitude of a wave?

  Sine
• What is the equation for the sine ratio?

  `sin θ = opposite / hypotenuse`
• The Pythagorean theorem states that in a right-angled triangle, a² + b² = c².


  True
• What is the Pythagorean theorem used for in right-angled triangles?

  Understanding their properties
• Trigonometry is used to resolve force vectors into horizontal and vertical components.


  True
• Vectors in physics have both magnitude and direction.


  True