Trigonometric ratios and the unit circle
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Trigonometric ratios and the unit circle. Mrs. White Precalculus 5.2/5.4. Schedule. Trig Ratios and the Unit Circle. Goals Students should be able to calculate the exact value of the 6 trigonometric ratios. Review – Complete the Table. Example 1.

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Trigonometric ratios and the unit circle

Trigonometric ratios and the unit circle

Mrs. WhitePrecalculus 5.2/5.4


Schedule

Schedule


Trig ratios and the unit circle

Trig Ratios and the Unit Circle

  • Goals

    • Students should be able to calculate the exact value of the 6 trigonometric ratios.


Review complete the table

Review – Complete the Table


Example 1

Example 1

  • Plot P (-12, -5) in the coordinate plane. If the terminal side of an angle in standard position passes through P, find the 6 trig. Ratios.


Example 2

Example 2

  • Plot P (5, -2) in the coordinate plane. If the terminal side of an angle in standard position passes through P, find the 6 trig. Ratios.


Example 3

Example 3

  • Given the following, find the 6 trigonometric ratios:

    • sec Θ = -2

    • sin Θ > 0


Example 4

Example 4

  • Find the reference angle, α.

  • Given:

  • Θ = 309o

  • α = 360o - 309o

  • α = 51o

  • Find the reference angle, α.

  • Given:

  • Θ =

  • Θ =

  • α =


Example 5

Example 5

  • Evaluate the 6 trig functions of the following angles. No Calculator.

  • Θ = 510°

  • This is coterminal with: 150°

  • Reference angle: 30°, Quadrant 2


Example 6

Example 6

  • Evaluate the 6 trig functions of the following angles. No Calculator.

  • Θ =

  • This is coterminal with:

  • Reference angle: , Quadrant 3


Example 7

Example 7

  • Sketch a right triangle corresponding to the trig function of the acute angle, Θ. Find the length of the missing side (using Pythagorean Th). Evaluate the remaining 5 trig. functions at Θ.

  • Given: Θ


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