14.2.3 Applying trigonometry in physics

• What is the ratio of sides for cosine (cos) in a right-angled triangle?

  Adjacent / Hypotenuse
• What is the ratio of sides for cosine (cos) in a right-angled triangle?

  Adjacent / Hypotenuse
• Sine (sin) is the ratio of the opposite side to the hypotenuse
• Steps to calculate side lengths using trigonometry in a right-angled triangle

  1️⃣ Identify the known side and angle

  2️⃣ Choose the appropriate trigonometric function

  3️⃣ Set up the equation

  4️⃣ Solve for the unknown side length
• Tangent (tan) is the ratio of the opposite side to the adjacent side.

  True
• The tangent (tan) is the ratio of the opposite side to the adjacent side.


  True
• What is the mathematical formula for tangent (tan) in terms of sides?

  \frac{opposite}{adjacent}</latex>
• What is trigonometry used for in physics?

  Relate sides and angles
• Tangent (tan) is the ratio of the opposite side to the adjacent side.


  True
• Tangent (tan) is the ratio of the opposite side to the adjacent side.


  True
• Cosine (cos) is the ratio of the adjacent side to the hypotenuse.


  True
• Sine (sin) is the ratio of the opposite side to the hypotenuse
• What is the ratio of sides used to define sine (sin)?

  Opposite / Hypotenuse
• What is the mathematical formula for sine (sin) in terms of sides?

  $\frac{opposite}{hypotenuse}$
• In a right-angled triangle with a hypotenuse of 10 cm, an opposite side of 6 cm, and an adjacent side of 8 cm, the sine of the angle is 0.6.


  True
• The cosine function in trigonometry is defined as the ratio of the adjacent side to the hypotenuse
• The value of cosine (cos) in a right-angled triangle where the adjacent side is 8 cm and the hypotenuse is 10 cm is 0.8
• What is the formula for tangent (tan) in terms of sine and cosine?

  \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}</latex>
• Steps to resolve a vector into its horizontal and vertical components

  1️⃣ Identify the angle between the vector and the horizontal axis

  2️⃣ Calculate the horizontal component using $V_{x} =$$V \cos(\theta)$

  3️⃣ Calculate the vertical component using $V_{y} =$$V \sin(\theta)$
• The vertical component of a vector with a magnitude of 20 units at an angle of 60° to the horizontal is 17.32 units.
• The horizontal component of a vector is calculated using $V_{x} =$$V \cos(\theta)$


  True
• What is the vertical component of a vector with magnitude 20 units at an angle of 60° to the horizontal?

  17.32 units
• The vertical velocity of a ball launched at 30 m/s at an angle of 45° to the horizontal is 21.21 m/s
• Match the trigonometric functions with their definitions:

  Sine (sin) ↔️ $\frac{\text{opposite}}{\text{hypotenuse}}$

  Cosine (cos) ↔️ $\frac{\text{adjacent}}{\text{hypotenuse}}$

  Tangent (tan) ↔️ $\frac{\text{opposite}}{\text{adjacent}}$
• What is the value of $\tan(\theta)$ in a right-angled triangle with opposite side 3 cm and adjacent side 4 cm?


  0.75
• In a right-angled triangle with hypotenuse 10 cm and angle 30°, what is the length of the opposite side?

  5 cm
• Resolving vectors involves breaking them into their horizontal and vertical components
• The vertical component $V_{y}$ for a vector $\mathbf{V}$ with magnitude 20 units and angle 60° to the horizontal is approximately 17.32 units.
• Which velocity component determines the maximum height of a projectile?

  $v_{y}$
• Trigonometry is essential for analyzing projectile motion because it allows us to break the initial velocity into its horizontal and vertical components.


  True
• A sinusoidal wave with amplitude 5 cm, frequency 10 Hz, and phase π/4 has the equation $y(t) =$$5 \sin(2 \pi \times 10 t + \frac{\pi}{4})$.π/4
• Sine (sin) is the ratio of the opposite side to the hypotenuse
• Sine (sin) is defined as the opposite side divided by the hypotenuse
• Why is understanding right-angled triangles crucial in physics?

  Involves angles
• What is the ratio of sides for tangent (tan) in a right-angled triangle?

  Opposite / Adjacent
• What is the ratio of sides for cosine (cos) in a right-angled triangle?

  Adjacent / Hypotenuse
• The ratio of the adjacent side to the hypotenuse defines the cosine
• The mathematical formula for cosine (cos) in terms of sides is $\frac{adjacent}{hypotenuse}$
• What ratio defines the sine function in trigonometry?

  Opposite / Hypotenuse
• The tangent function in trigonometry is the ratio of the opposite side to the adjacent side.


  True