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MAT 103 Dr. Wright-Test 1 Flashcard Deck

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Termini in questo insieme (20)

  • What is the supplement of a 100° angle?
    The supplement is \(80^\circ\) because supplementary angles add up to \(180^\circ\).
  • How to find the smallest positive coterminal angle of 868°?
    Subtract multiples of \(360^\circ\) until the angle is between 0° and 360°. The smallest positive coterminal angle is 148°.
  • What is the sum of angles in a triangle?
    The sum of the interior angles in any triangle is always \(180^\circ\).
  • How to find the third angle of a triangle if two angles are 40° and 97°?
    Subtract the sum of the two angles from 180°. The third angle is \(43^\circ\).
  • What is the relationship between similar triangles?
    Corresponding angles are equal and corresponding sides are proportional.
  • How to find the height of a tree using shadows and similar triangles?
    Use the ratio of the post's height to its shadow length to find the tree's height from its shadow length.
  • How to find cotangent given a point (-7, 2) on the terminal side of angle θ?
    Cotangent is the ratio of x to y: \(\cot \theta = \frac{x}{y} = \frac{-7}{2}\).
  • How to find the exact value of a trigonometric function given coordinates on the terminal side?
    Use the definitions: sin = y/r, cos = x/r, tan = y/x, where r = sqrt(x² + y²).
  • What is the value of sin(180°) + cos(180°)?
    sin(180°) = 0 and cos(180°) = -1, so the sum is -1.
  • How to identify the quadrant of an angle if sec(θ) < 0 and tan(θ) < 0?
    sec(θ) < 0 means cos(θ) < 0, tan(θ) < 0 means sin(θ)/cos(θ) < 0, so θ is in Quadrant II.
  • How to find sin(θ) given cos(θ) = 4/9 and θ in Quadrant IV?
    Use Pythagorean identity: sin²(θ) = 1 - cos²(θ). Since θ is in Quadrant IV, sin(θ) is negative.
  • How to solve tan(3θ + 57°) = cot(θ + 15°) for acute angles?
    Use cot(α) = tan(90° - α) and solve the resulting equation for θ.
  • How to find all θ in [0°, 360°) where sin(θ) = 3/2?
    Since sin(θ) cannot be greater than 1, no solution exists for sin(θ) = 3/2.
  • How to convert degrees to radians? Example: 430°
    Multiply degrees by \(\frac{\pi}{180}\\). 430° = \(\frac{43\pi}{18}\) radians.
  • How to convert radians to degrees? Example: \(\frac{7\pi}{10}\)
    Multiply radians by \(\frac{180}{\pi}\). \(\frac{7\pi}{10}\) = 126°.
  • Formula for length of an arc intercepted by central angle θ in a circle of radius r
    Arc length = r × θ, where θ is in radians.
  • Formula for area of a sector with radius r and central angle θ (radians)
    Area = \(\frac{1}{2} r^2 \theta\).
  • How to find distance between two points on Earth's surface given central angle and radius?
    Distance = radius × central angle (in radians).
  • How to find exact value of tan(π/3)?
    tan(π/3) = \(\sqrt{3}\).
  • How to find angular velocity ω given linear velocity v and radius r?
    ω = v / r.