Trigonometry Skills

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  • Unit Circle
    • Degrees
      • Determine trig function values, unit circle, first quadrant, degrees, sin, cos, & tan, exact answers
      • Determine trig function values, unit circle, second quadrant, degrees, sin, cos, & tan, exact answers
      • Determine trig function values, unit circle, third quadrant, degrees, sin, cos, & tan, exact answers
      • Determine trig function values, unit circle, fourth quadrant, degrees, sin, cos, & tan, exact answers
      • Determine trig function values, unit circle, axes, degrees, sin, cos, & tan, exact answers
      • Determine sine values, unit circle, degrees, exact answers
      • Determine cosine values, unit circle, degrees, exact answers
      • Determine tangent values, unit circle, degrees, exact answers
      • Determine trig function values, unit circle, degrees, sin, cos, & tan, exact answers
    • Radians
      • Determine trig function values, unit circle, first quadrant, radians, sin, cos, & tan, exact answers
      • Determine trig function values, unit circle, second quadrant, radians, sin, cos, & tan, exact answers
      • Determine trig function values, unit circle, third quadrant, radians, sin, cos, & tan, exact answers
      • Determine trig function values, unit circle, fourth quadrant, radians, sin, cos, & tan, exact answers
      • Determine trig function values, unit circle, axes, radians, sin, cos, & tan
      • Determine sine values, unit circle, radians, exact answers
      • Determine cosine values, unit circle, radians, exact answers
      • Determine tangent values, unit circle, radians, exact answers
      • Determine trig function values, unit circle, radians, sin, cos, & tan, exact answers
      • Given arc length & radius, determine radian measure
    • Radians & Degrees
      • Convert degrees to radians
      • Convert radians to degrees
      • Condensed: Convert between degrees & radians
      • Determine trig function values, unit circle, sin, cos, & tan, exact answers
      • Determine trig function values, unit circle, cot, csc, & sec, exact answers
  • Special Right Triangles
    • 30-60-90 Triangles
      • Given 30-60-90 triangle & short leg, determine hypotenuse
      • Given 30-60-90 triangle & short leg, determine long leg
      • Given 30-60-90 triangle & long leg, determine short leg
      • Given 30-60-90 triangle & long leg, determine hypotenuse
      • Given 30-60-90 triangle & hypotenuse, determine short leg
      • Given 30-60-90 triangle & hypotenuse, determine long leg
      • Given 30-60-90 triangle, determine side
    • 45-45-90 Triangles
      • Given 45-45-90 triangle, determine hypotenuse
      • Given 45-45-90 triangle, determine leg
      • Given 45-45-90 triangle, determine side
    • Application of Special Right Triangles
      • Condensed: Given special right triangle, determine side
      • Determine sides using special right triangle relationships, real-world context
      • Determine angles using special right triangle relationships, real-world context
      • Condensed: Determine angles or sides using special right triangle relationships, real-world context
  • Trigonometric Ratios & Solving Right Triangles
    • Trigonometric Ratios
      • Identify definitions of trig functions
      • Determine relationship between trig ratios of sides of similar triangles, sin, cos, & tan
      • Given special right triangle, determine trig function value, sin, cos, & tan
      • Given special right triangle, determine trig function value, cot, sec, & csc
      • Condensed: Given special right triangle, determine trig function value
      • Given right triangle, determine trig ratio, sin, cos, & tan
      • Given right triangle, determine trig ratio, cot, sec, & csc
      • Condensed: Given right triangle, determine trig ratio
      • Given right triangle, determine missing side & trig ratio, sin, cos, & tan
      • Given right triangle, determine missing side & trig ratio, cot, sec, & csc
      • Condensed: Given right triangle, determine missing side & trig ratio
    • Evaluating Trigonometric Functions
      • Given sine, cosine, or tangent & quadrant, determine trig function values
      • Determine trig function values, degrees, calculator expected
      • Determine trig function values, radians, calculator expected
      • Condensed: Determine trig function values, calculator expected
    • Solving Right Triangles
      • Solving Sides of Triangles
        • Determine hypotenuse of right triangle using sine
        • Determine leg of right triangle using sine
        • Given side & angle, determine specified side using sine
        • Determine hypotenuse of right triangle using cosine
        • Determine leg of right triangle using cosine
        • Given side & angle, determine specified side using cosine
        • Given long leg of right triangle, determine short leg using tangent
        • Given short leg of right triangle, determine long leg using tangent
        • Given side & angle, determine specified side using tangent
        • Condensed: Given side & angle, determine specified side using sine, cosine, or tangent
      • Solving Angles of Triangles
        • Given hypotenuse & leg of right triangle, determine angle using arcsine
        • Given hypotenuse & leg of right triangle, determine angle using arccosine
        • Given legs of right triangle, determine angle using arctangent
        • Given sides of triangle, determine angle using arcsine, arccosine, or arctangent
      • Application of Right Triangles
        • Given right triangle, determine side, real-world context
        • Given right triangle, determine angle, real-world context
        • Given legs of right triangle, determine angle using arctangent, real-world context
        • Condensed: Given right triangle, determine sides or angles, real-world context
      • Complementary Angle
        • Determine equivalent trig cofunction values, sin & cos
        • Determine equivalent trig cofunction values, tan & cot
        • Determine equivalent trig cofunction values, sec & csc
        • Determine equivalent trig cofunction values from triangles
        • Condensed: Determine equivalent trig cofunction values
  • Trigonometric Identities
    • Determine missing steps in proofs of Pythagorean identities
  • Law of Sines & Law of Cosines
    • Determine sides of triangles using law of sines
    • Determine angles of triangles using law of sines
    • Determine sides or angles of triangles using law of sines, multiple choice
    • Condensed: Determine sides & angles of triangles using law of sines
    • Determine sides & angles of triangles using law of sines, real-world context
    • Determine sides of triangles using law of cosines
    • Determine angles of triangles using law of cosines
    • Determine sides or angles of triangles using law of cosines, multiple choice
    • Condensed: Determine sides & angles of triangles using law of cosines
    • Determine sides & angles of triangles using law of cosines, real-world context
    • Condensed: Determine sides & angles of triangles using law of sines or law of cosines, real-world context
    • Determine area of triangles using sine formula
  • Graphing Trigonometric Functions
    • Given graph or equation, determine amplitude of trig function
    • Given graph or equation, determine midline of trig function
    • Given graph or equation, determine period of trig function
    • Condensed: Given graph or equation, determine characteristics of trig function
    • Determine graph of trig functions, sin, one transformation
    • Determine graph of trig functions, sin, multiple transformations
    • Determine graph of trig functions, cos, one transformation
    • Determine graph of trig functions, cos, multiple transformations
    • Determine graph of trig functions, tan & cot
    • Determine graph of trig functions, sec & csc
    • Identify trigonometric functions to model periodic data, real-world context