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Questions and Answers
What is the value of cos²(A) in terms of sin(A) using the Pythagorean Identity?
What is the formula for the sine of the sum of two angles?
What is the measure of central tendency that is most affected by outliers in a dataset?
What is the purpose of a confidence interval in inferential statistics?
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What is the value of sin(2A) in terms of sin(A) and cos(A)?
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What is the difference between the largest and smallest values in a dataset?
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What is the type of error that occurs when a false null hypothesis is not rejected?
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What is the formula for the cosine of the sum of two angles?
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What is the purpose of the alternative hypothesis in a hypothesis test?
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What is the formula for the tangent of an angle in terms of sine and cosine?
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Study Notes
Trigonometry
Angles and Triangles
- Angles can be measured in degrees, radians, or gradians
- Triangles can be classified as right-angled, acute-angled, or obtuse-angled
- Pythagorean Identity: sin²(A) + cos²(A) = 1
Trigonometric Ratios
- Sine (sin): opposite side / hypotenuse
- Cosine (cos): adjacent side / hypotenuse
- Tangent (tan): opposite side / adjacent side
- Cotangent (cot): adjacent side / opposite side
- Secant (sec): hypotenuse / opposite side
- Cosecant (csc): hypotenuse / adjacent side
Identities and Formulas
- Sum and Difference Formulas:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- Double Angle Formulas:
- sin(2A) = 2sin(A)cos(A)
- cos(2A) = cos²(A) - sin²(A)
- Half Angle Formulas:
- sin(A/2) = ±√((1 - cos(A))/2)
- cos(A/2) = ±√((1 + cos(A))/2)
Statistics
Descriptive Statistics
- Measures of Central Tendency:
- Mean (μ): average value of a dataset
- Median (M): middle value of a dataset when arranged in order
- Mode: most frequently occurring value in a dataset
- Measures of Variability:
- Range: difference between the largest and smallest values
- Interquartile Range (IQR): difference between the 75th and 25th percentiles
- Variance (σ²): average of the squared differences from the mean
- Standard Deviation (σ): square root of the variance
Inferential Statistics
- Hypothesis Testing:
- Null Hypothesis (H0): statement of no significant difference or relationship
- Alternative Hypothesis (H1): statement of significant difference or relationship
- Confidence Intervals:
- Interval estimate of a population parameter
- Margin of Error (ME): maximum amount by which the sample statistic may differ from the population parameter
- Types of Errors:
- Type I Error (α): rejecting a true null hypothesis
- Type II Error (β): failing to reject a false null hypothesis
Trigonometry
Angles and Triangles
- Angles can be measured in three units: degrees, radians, or gradians
- Triangles are classified into three types: right-angled, acute-angled, and obtuse-angled
- The Pythagorean Identity is a fundamental concept: sin²(A) + cos²(A) = 1
Trigonometric Ratios
- Sine (sin) is the ratio of the opposite side to the hypotenuse
- Cosine (cos) is the ratio of the adjacent side to the hypotenuse
- Tangent (tan) is the ratio of the opposite side to the adjacent side
- Cotangent (cot) is the ratio of the adjacent side to the opposite side
- Secant (sec) is the ratio of the hypotenuse to the opposite side
- Cosecant (csc) is the ratio of the hypotenuse to the adjacent side
Identities and Formulas
- Sum and Difference Formulas for sine and cosine:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- Double Angle Formulas for sine and cosine:
- sin(2A) = 2sin(A)cos(A)
- cos(2A) = cos²(A) - sin²(A)
- Half Angle Formulas for sine and cosine:
- sin(A/2) = ±√((1 - cos(A))/2)
- cos(A/2) = ±√((1 + cos(A))/2)
Statistics
Descriptive Statistics
- Measures of Central Tendency:
- Mean (μ) is the average value of a dataset
- Median (M) is the middle value of a dataset when arranged in order
- Mode is the most frequently occurring value in a dataset
- Measures of Variability:
- Range is the difference between the largest and smallest values
- Interquartile Range (IQR) is the difference between the 75th and 25th percentiles
- Variance (σ²) is the average of the squared differences from the mean
- Standard Deviation (σ) is the square root of the variance
Inferential Statistics
- Hypothesis Testing:
- Null Hypothesis (H0) states no significant difference or relationship
- Alternative Hypothesis (H1) states significant difference or relationship
- Confidence Intervals:
- Interval estimate of a population parameter
- Margin of Error (ME) is the maximum amount by which the sample statistic may differ from the population parameter
- Types of Errors:
- Type I Error (α) occurs when a true null hypothesis is rejected
- Type II Error (β) occurs when a false null hypothesis is not rejected
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Description
This quiz covers the fundamentals of trigonometry, including measuring angles, classifying triangles, and understanding trigonometric ratios.
