14.2.3 Applying trigonometry in physics

Cards (66)

  • 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?
    a2+a^{2} +b2= b^{2} =c2 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, a2+a^{2} +b2= b^{2} =c2 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 ↔️ sinθ=\sin \theta =oppositehypotenuse \frac{\text{opposite}}{\text{hypotenuse}}
    Cosine ↔️ cosθ=\cos \theta =adjacenthypotenuse \frac{\text{adjacent}}{\text{hypotenuse}}
    Tangent ↔️ tanθ=\tan \theta =oppositeadjacent \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 = .

    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