10 Questions
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 $b$.
True
Trigonometry is only used in navigation and surveying.
False
The tangent function is defined as the opposite side over the hypotenuse.
False
Oblique triangles always have one 90-degree angle.
False
The trigonometric ratio $cosine = opposite side / hypotenuse$ is correct.
False
The CAST mnemonic device is used to remember the order of trigonometric identities.
False
The equation $2sin^2(x) - 3sin(x) = 0$ is a linear trigonometric equation.
False
The trigonometric identity $sin^2(x) + cos^2(x) = -1$ is true for all values of $x$.
False
Trigonometry is only used to solve right triangles.
False
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.
Test your knowledge of trigonometric equations, including solving equations and identities involving sine, cosine, and tangent functions.
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