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Trig Functions of Any Angle | Plotting Points, Triangles, and Reference Angles

Learn how to plot points, create triangles, and find reference angles for trigonometric functions of any angle. Understand the concept of quadrants and how they affect the reference angles.

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Trig Functions of Any Angle | Plotting Points, Triangles, and Reference Angles

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  1. Section 4.4

  2. Trigonometric Functions of Any Angle • If you are given an ordered pair that is not on the Unit Circle, then you need to plot the point. • From the point you plotted, make a right triangle. Draw a vertical line from the point to the x-axis. Draw a diagonal line from the point to the origin.

  3. Trigonometric Functions of Any Angle • Label the x-coordinate on the x-axis and the y-coordinate on the side of the triangle that is vertical. • Theta goes inside the triangle closest to the origin. • Use Pythagorean Theorem to find the third side of the triangle. The hypotenuse is always positive.

  4. Trigonometric Functions of Any Angle • Use right triangle trigonometry to find the six trigonometric functions.

  5. Reference Angles • Reference Angles – the distance from the terminal side of the angle to the x-axis. • Reference angles are always acute and always positive.

  6. Reference Angles • Quadrant I: • Quadrant II: • Quadrant III: • Quadrant IV:

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