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14. Practical skills and data analysis
14.2 Mathematical skills
14.2.3 Applying trigonometry in physics
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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?
a
2
+
a^{2} +
a
2
+
b
2
=
b^{2} =
b
2
=
c
2
c^{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
+
a^{2} +
a
2
+
b
2
=
b^{2} =
b
2
=
c
2
c^{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
θ
=
\sin \theta =
sin
θ
=
opposite
hypotenuse
\frac{\text{opposite}}{\text{hypotenuse}}
hypotenuse
opposite
Cosine ↔️
cos
θ
=
\cos \theta =
cos
θ
=
adjacent
hypotenuse
\frac{\text{adjacent}}{\text{hypotenuse}}
hypotenuse
adjacent
Tangent ↔️
tan
θ
=
\tan \theta =
tan
θ
=
opposite
adjacent
\frac{\text{opposite}}{\text{adjacent}}
adjacent
opposite
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
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