Podcast
Questions and Answers
The equation $sin(x) = 1/2$ has a unique solution.
The equation $sin(x) = 1/2$ has a unique solution.
False
The trigonometric identity $cos(a + b) = cos(a)cos(b) + sin(a)sin(b)$ is true for all values of $a$ and $b$.
The trigonometric identity $cos(a + b) = cos(a)cos(b) + sin(a)sin(b)$ is true for all values of $a$ and $b$.
True
Trigonometry is only used in navigation and surveying.
Trigonometry is only used in navigation and surveying.
False
The tangent function is defined as the opposite side over the hypotenuse.
The tangent function is defined as the opposite side over the hypotenuse.
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Oblique triangles always have one 90-degree angle.
Oblique triangles always have one 90-degree angle.
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The trigonometric ratio $cosine = opposite side / hypotenuse$ is correct.
The trigonometric ratio $cosine = opposite side / hypotenuse$ is correct.
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The CAST mnemonic device is used to remember the order of trigonometric identities.
The CAST mnemonic device is used to remember the order of trigonometric identities.
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The equation $2sin^2(x) - 3sin(x) = 0$ is a linear trigonometric equation.
The equation $2sin^2(x) - 3sin(x) = 0$ is a linear trigonometric equation.
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The trigonometric identity $sin^2(x) + cos^2(x) = -1$ is true for all values of $x$.
The trigonometric identity $sin^2(x) + cos^2(x) = -1$ is true for all values of $x$.
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Trigonometry is only used to solve right triangles.
Trigonometry is only used to solve right triangles.
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Study Notes
Trigonometry
Equations
- Trigonometric equations involve trigonometric functions such as sine, cosine, and tangent.
- Solving trigonometric equations often involves using identities and algebraic manipulation.
- Examples of trigonometric equations:
- sin(x) = 1/2
- 2cos^2(x) - 3sin(x) = 0
Identities
- Trigonometric identities are equations that are true for all values of the variables.
- Examples of trigonometric identities:
- sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
- cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
- sin^2(x) + cos^2(x) = 1
Applications
- Trigonometry has many real-world applications, including:
- Navigation and surveying
- Physics and engineering
- Computer graphics and game development
- Medical imaging and analysis
Functions
- Trigonometric functions:
- Sine (sin): opposite side over hypotenuse
- Cosine (cos): adjacent side over hypotenuse
- Tangent (tan): opposite side over adjacent side
- Cotangent (cot): adjacent side over opposite side
- Secant (sec): hypotenuse over adjacent side
- Cosecant (csc): hypotenuse over opposite side
Triangles
- Trigonometry is used to solve triangles, which involve:
- Angles and side lengths
- Right triangles (one 90-degree angle)
- Oblique triangles (no 90-degree angle)
Ratios
- Trigonometric ratios:
- sine = opposite side / hypotenuse
- cosine = adjacent side / hypotenuse
- tangent = opposite side / adjacent side
- cotangent = adjacent side / opposite side
CAST
- CAST is a mnemonic device to remember the order of trigonometric functions:
- C - Cosine
- A - And
- S - Sine
- T - Tangent
Trigonometry
Equations
- Trigonometric equations involve trigonometric functions like sine, cosine, and tangent.
- Solving trigonometric equations often involves using identities and algebraic manipulation.
- Examples of trigonometric equations include sin(x) = 1/2 and 2cos^2(x) - 3sin(x) = 0.
Identities
- Trigonometric identities are equations that are true for all values of the variables.
- Examples of trigonometric identities include sin(a + b) = sin(a)cos(b) + cos(a)sin(b) and cos(a + b) = cos(a)cos(b) - sin(a)sin(b).
- Another example of a trigonometric identity is sin^2(x) + cos^2(x) = 1.
Applications
- Trigonometry has many real-world applications, including navigation and surveying.
- Trigonometry is also used in physics and engineering.
- Other applications include computer graphics and game development, as well as medical imaging and analysis.
Functions
- Trigonometric functions include sine, cosine, and tangent.
- Sine is defined as the opposite side over the hypotenuse.
- Cosine is defined as the adjacent side over the hypotenuse.
- Tangent is defined as the opposite side over the adjacent side.
- Other trigonometric functions include cotangent, secant, and cosecant.
- Cotangent is defined as the adjacent side over the opposite side.
- Secant is defined as the hypotenuse over the adjacent side.
- Cosecant is defined as the hypotenuse over the opposite side.
Triangles
- Trigonometry is used to solve triangles, which involve angles and side lengths.
- There are two main types of triangles: right triangles and oblique triangles.
- Right triangles have one 90-degree angle, while oblique triangles do not.
Ratios
- Trigonometric ratios include sine, cosine, and tangent.
- Sine is defined as the opposite side over the hypotenuse.
- Cosine is defined as the adjacent side over the hypotenuse.
- Tangent is defined as the opposite side over the adjacent side.
- There are also three other trigonometric ratios: cotangent, secant, and cosecant.
- Cotangent is defined as the adjacent side over the opposite side.
- Secant is defined as the hypotenuse over the adjacent side.
- Cosecant is defined as the hypotenuse over the opposite side.
CAST
- CAST is a mnemonic device to remember the order of trigonometric functions.
- CAST stands for Cosine, And, Sine, and Tangent.
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Description
Test your knowledge of trigonometric equations, including solving equations and identities involving sine, cosine, and tangent functions.
