Trigonometry Basics

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Questions and Answers

What is the value of cos²(A) in terms of sin(A) using the Pythagorean Identity?

  • 1 - sin²(A) (correct)
  • 1 - sin(A)
  • sin²(A) / (1 - sin²(A))
  • 1 / sin²(A)

What is the formula for the sine of the sum of two angles?

  • sin(A) - sin(B)
  • sin(A)cos(B) + cos(A)sin(B) (correct)
  • sin(A) + sin(B)
  • sin(A)cos(B) - cos(A)sin(B)

What is the measure of central tendency that is most affected by outliers in a dataset?

  • Mean (correct)
  • Median
  • Mode
  • Range

What is the purpose of a confidence interval in inferential statistics?

<p>To estimate a population parameter (D)</p> Signup and view all the answers

What is the value of sin(2A) in terms of sin(A) and cos(A)?

<p>2sin(A)cos(A) (B)</p> Signup and view all the answers

What is the difference between the largest and smallest values in a dataset?

<p>Range (D)</p> Signup and view all the answers

What is the type of error that occurs when a false null hypothesis is not rejected?

<p>Type II Error (A)</p> Signup and view all the answers

What is the formula for the cosine of the sum of two angles?

<p>cos(A)cos(B) - sin(A)sin(B) (B)</p> Signup and view all the answers

What is the purpose of the alternative hypothesis in a hypothesis test?

<p>To state a significant difference or relationship (B)</p> Signup and view all the answers

What is the formula for the tangent of an angle in terms of sine and cosine?

<p>sin(A) / cos(A) (B)</p> Signup and view all the answers

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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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