Sin Cos Tan Graphs

• What is the radius of the unit circle?

  1 unit
• What do sine, cosine, and tangent help us understand?

  The relationship between angles and sides in a right triangle
• What are the sine, cosine, and tangent values for a right triangle with angle θ, opposite side = 3, adjacent side = 4, and hypotenuse = 5?

  • sin θ = $\frac{3}{5}$
  • cos θ = $\frac{4}{5}$
  • tan θ = $\frac{3}{4}$
• What are the three trigonometric functions defined in the material?

  Sine, cosine, and tangent
• Where does the sine graph pass through?

  Origin
• How are sine, cosine, and tangent defined in a right triangle?

  Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent
• What are the key features of the sin graph?

  • The graph does not start at the origin but it does pass through it
  • The graph is continuous and repeats every 360°
  • The maximum value is 1 and the minimum value is -1
• What do sine, cosine, and tangent represent on the unit circle?

  Sine = y-coordinate, Cosine = x-coordinate, Tangent = y-coordinate / x-coordinate
• What do the coordinates (x, y) represent on the unit circle?

  (cos θ, sin θ)
• How do the definitions of sine, cosine, and tangent differ between a right triangle and the unit circle?

  Right triangle uses sides; unit circle uses coordinates
• What does the horizontal axis of a trigonometric graph represent?

  The angle, usually written as θ
• What does the y-coordinate represent in the unit circle?

  Sine
• Why is understanding the unit circle important?

  It shows how sine, cosine, and tangent relate
• What is the period of the tangent function?

  180°
• What is a sin graph?

  A visual representation of the sine function for a given range of angles
• What does the horizontal axis of a sine graph represent?

  Angles (θ)
• What is the significance of asymptotes in tangent graphs?

  They indicate where the function approaches infinity
• What does the horizontal axis of a trigonometric graph represent?

  The angle, usually written as θ
• What is a tan graph?

  A visual representation of the tangent function for a given range of angles
• How do the coordinates on the unit circle relate to angles?

  They represent the sine and cosine of angles
• What is the amplitude of the sine function?

  1
• What are the key features of the unit circle?

  • Radius: 1 unit
  • x-coordinate: Represents cosine
  • y-coordinate: Represents sine
• What are the key features of the cosine function graph?

  • Periodic function with period 2π
  • Oscillates between 1 and -1 on the y-axis
  • Peaks at $\frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, ...$
  • Troughs at $-\frac{\pi}{2}, -\frac{3\pi}{2}, -\frac{5\pi}{2}, ...$
• What are the key features of sine graphs?

  • Horizontal axis represents angles (θ)
  • Vertical axis shows sine values
  • Continuous curve
  • Passes through origin
  • Oscillates between -1 and 1
• What type of graph does the sine function create?

  Wave-like graph
• How is tangent defined in terms of sine and cosine on the unit circle?

  tan θ = y / x
• What does the y-axis of a trigonometric graph represent?

  The tangent function of that angle
• Does the tangent function have asymptotes?

  Yes
• What characteristic describes the curve of a sine graph?

  It is a continuous curve
• How does the unit circle help in trigonometry?

  It helps understand sine, cosine, and tangent
• What are the key features of tangent graphs compared to sine and cosine graphs?

  • Period: Tangent = 180°, Sine/Cosine = 360°
  • Asymptotes: Tangent has them, Sine/Cosine do not
  • Curve Type: Tangent is discontinuous, Sine/Cosine are continuous
• What are the key properties of a tan graph?

  • Repeats every 180°
  • Not a continuous curve
  • Vertical asymptotes at 90° ± 180°
• What are the key properties of the tangent function?

  • Period: $\pi$
  • Asymptotes: Vertical lines
  • Range: All real numbers
  • Shape: S-curve between asymptotes
• How are different amplitudes represented in sine wave equations?

  • The equation is $y =$$A \sin(x)$
  • A controls the height of the wave
• What does the y-axis of a trigonometric graph represent?

  The sine function of that angle
• How does the curve type of the tangent function differ from sine and cosine?

  Tangent is discontinuous, sine and cosine are continuous
• What does it mean for the sine function to be periodic?

  It repeats every 360°
• Are sine and cosine functions discontinuous or continuous?

  Continuous
• What is the relationship between the three waveforms?

  • Wave 1 and Wave 2 are individual waveforms
  • The Mix waveform is a combination of Wave 1 and Wave 2
• What does the amplitude of a sine wave control?

  Its vertical height