The three main trigonometric functions are sine, cosine, and tangent
What is the key skill in applying trigonometry in physics?
Solving right-angled triangles
Physical quantities such as vectors, forces, and displacements can be represented using right-angled triangles.
True
By recognizing right-angled triangle representations in physics problems, you can apply trigonometric functions to calculate unknown sides or angles
What type of triangle is required for applying sine, cosine, and tangent functions?
Right-angled triangle
If you know the magnitude of a force and its angle with the horizontal, which trigonometric functions can you use to find its components?
Sine and cosine
If you know the magnitude of a force and the angle it makes with the horizontal, you can use the sine or cosine function to find the horizontal and vertical components
What is the definition of sine in a right-angled triangle?
Opposite / Hypotenuse
The trigonometric functions are mathematical relationships between the sides and angles of a right-angled triangle
How are vectors represented as right-angled triangles in physics problems?
Horizontal and vertical components
The trigonometric functions sine, cosine, and tangent can be used to solve for unknown sides or angles in a right-angled triangle.
True
Which trigonometric function is used to find the vertical component of a vector?
Sine
The sine or cosine function is used to find the horizontal and vertical components of a force
What does the sine function represent in a right-angled triangle?
Opposite/Hypotenuse
The sine function is used to find the vertical component of a vector
The cosine function is used to find the horizontal component of a vector.
True
If a vector has a magnitude of 10 units and an angle of 30° to the horizontal, its horizontal component is 10 × cos(30°) = 8.66
Breaking down a vector into its right-angled triangle components allows for more effective analysis in physics problems.
True
In wave calculations, the amplitude of a wave can be represented by the opposite side of a right-angled triangle
Projectile motion problems can be solved using trigonometry by representing the motion as a right-angled triangle.
True
What does the sine function help find in projectile motion problems?
Vertical velocity
Match the trigonometric function with its application in projectile motion:
Sine ↔️ Vertical velocity
Cosine ↔️ Horizontal velocity
Tangent ↔️ Launch angle
The cosine function is used to find the horizontal component of a projectile's initial velocity.
What is the horizontal component of a projectile launched with an initial velocity of 50 m/s at an angle of 30° to the horizontal?
43.3 m/s
Match the trigonometric function with its application in projectile motion:
Sine ↔️ Vertical component
Cosine ↔️ Horizontal component
Tangent ↔️ Launch angle
The cosine function represents the ratio of the adjacent side to the hypotenuse in a right-angled triangle.
What physical quantity can be represented using a right-angled triangle in physics problems?
Vectors
The cosine function is the ratio of the adjacent side to the hypotenuse.
True
The horizontal component of a vector with magnitude 10 units and an angle of 30° to the horizontal is 8.66 units.
The sine function is used to find the vertical component of a vector.
What is the horizontal component of a vector with magnitude 10 units and an angle of 30° to the horizontal?
8.66 units
Steps to solve wave problems using trigonometry
1️⃣ Represent wave properties using right-angled triangles
2️⃣ Identify the known side length and angle
3️⃣ Use the appropriate trigonometric function
4️⃣ Calculate the unknown wave property
The tangent function is used to find the launch angle of a projectile.
True
Trigonometry is essential for calculating the time of flight and range of a projectile.
True
What is the vertical component of a force of 10 N at 30° to the horizontal in an electric field?
5 N
What are the trigonometric functions relationships between?
Sides and angles
Match the trigonometric function with its definition:
Sine (sin) ↔️ Ratio of the opposite side to the hypotenuse
Cosine (cos) ↔️ Ratio of the adjacent side to the hypotenuse
Tangent (tan) ↔️ Ratio of the opposite side to the adjacent side
Understanding basic trigonometry concepts is essential for solving physics problems involving vectors, forces, and other quantities represented using right-angled triangles
What is the displacement of an object broken down into when analyzing motion?
Horizontal and vertical components
Steps in resolving a force vector into perpendicular components