Trigonometry Basics

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