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Finding the Exact Value of Trigonometric Functions

Finding the Exact Value of Trigonometric Functions. Review: Special Right Triangles. Find the missing side Lengths:. 60 °. π / 3. 1. 45°. π / 4. 1. π / 6. 30 °. π / 4. 45 °. Important Points on Unit Circle. 1. π / 2. 90 °. 2 π / 3. π / 3. 120 °. 60 °. 3 π / 4. π / 4.

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Finding the Exact Value of Trigonometric Functions

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  1. Finding the Exact Value of Trigonometric Functions

  2. Review: Special Right Triangles Find the missing side Lengths: 60° π / 3 1 45° π / 4 1 π / 6 30° π / 4 45°

  3. Important Points on Unit Circle 1 π / 2 90° 2π / 3 π / 3 120° 60° 3π / 4 π / 4 135° 45° 5π / 6 π / 6 150° 30° π 0 0° 180° -1 1 11π / 6 7π / 6 330° 210° 7π / 4 5π / 4 315° 225° 5π / 3 4π / 3 300° 240° 3π / 2 270° -1

  4. 1 60° 1/2 1 1 1/2 45° 30° Important Points on Unit Circle 1 π / 2 2π / 3 π / 3 3π / 4 π / 4 5π / 6 π / 6 π 0 -1 1 11π / 6 7π / 6 7π / 4 5π / 4 5π / 3 4π / 3 3π / 2 -1

  5. Important Points on Unit Circle 1 90° 120° 60° 135° 45° 150° 30° 0° 180° -1 1 330° 210° 315° 225° 300° 240° 270° -1

  6. Important Points on Unit Circle 1 π / 2 2π / 3 π / 3 3π / 4 π / 4 5π / 6 π / 6 π 0 -1 1 11π / 6 7π / 6 7π / 4 5π / 4 5π / 3 4π / 3 3π / 2 -1

  7. Reference Angle On the left are 3 reference angles that we know exact trig values for. To find the reference angle for angles not in the 1st quadrant (the angles at right), ignore the integer in the numerator. Then multiply the number in the numerator by the degree to find the angle’s quadrant.

  8. Stewart’s Table: Finding Exact Values of Trig Functions • Find the value of the Reference Angle. • Find the angles quadrant to figure out the sign (+/-). Each time the square root number goes up by 1 Reverse the order of the values from sine

  9. Example 1 Find the exact value of the following:

  10. Example 2 Solve: π / 6 π / 6

  11. Slope on the Unit Circle What is the slope of the terminal side of an angle on the unit circle? 1 (cosӨ,sinӨ) sinӨ Opposite Ө -1 1 cosӨ Adjacent Slope = -1

  12. A Definition of Tangent The tangent function is defined as: There are values for which the tangent function are undefined: Any Θ that makes cos(Θ)=0. In general: For any integer n.

  13. Stewart’s Table: Finding Exact Values of Trig Functions • Find the value of the Reference Angle. • Find the angles quadrant to figure out +/-. Each time the square root number goes up by 1 Reverse the order of the values from sine

  14. Example 3 Find the exact value of the following: Thought process The only thing required for a correct answer (unless the question says explain)

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