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Definition: Reference Angle - A positive acute angle found between the terminal side of an angle in standard position and the x-axis.

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Presentation on theme: "Definition: Reference Angle - A positive acute angle found between the terminal side of an angle in standard position and the x-axis."— Presentation transcript:

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2 Definition: Reference Angle - A positive acute angle found between the terminal side of an angle in standard position and the x-axis.

3 Examples: Determine the reference angle of the following angles: = 65 Lets draw a picture: Lets see where the reference angle is… Terminal side Reference Angle Lets calculate the reference angle… = 65

4 Examples: Determine the reference angle of the following angles: = 192 Lets draw a picture: Lets see where the reference angle is… Terminal side Reference Angle Lets calculate the reference angle… = 192 - 180 = 12

5 Examples: Determine the reference angle of the following angles: = 119 Lets draw a picture: Lets see where the reference angle is… Terminal side Reference Angle Lets calculate the reference angle… = 180 - 119 = 61

6 Examples: Determine the reference angle of the following angles: = 341 Lets draw a picture: Lets see where the reference angle is… Terminal side Reference Angle Lets calculate the reference angle… = 360 - 341 = 19

7 Examples: Determine the reference angle of the following angles: = / 9 Lets draw a picture: Lets see where the reference angle is… Terminal side Reference Angle Lets calculate the reference angle… = / 9

8 Examples: Determine the reference angle of the following angles: = 7 / 5 Lets draw a picture: Lets see where the reference angle is… Terminal side Reference Angle Lets calculate the reference angle… = 7 / 5 - = 2 / 5

9 Examples: Determine the reference angle of the following angles: = -3 / 8 Lets draw a picture: Lets see where the reference angle is… Terminal side Reference Angle Lets calculate the reference angle… = 2 - 13 / 8 = 3 / 8 We need to first find a coterminal angle: -3 / 8 + 2 -3 / 8 + 16 / 8 13 / 8

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11 Now that you have been exposed to the concept of reference angle, it is time to finish this section. We can now determine trigonometric values of non-acute angles.

12 Example: Let (-3,4) be a point on the terminal side of (in standard position). Determine the sine, cosine and tangent of. Step 1: Draw a picture of the situation. (-3,4) Step2: Draw the reference triangle (drop the altitude to the x-axis). Then determine the lengths of the sides of the reference triangle. 3 4 Determine the radius of the circle passing through the point referenced. Step 3: Use the non-unit circle definitions to determine the values of the trig. functions requested. sin = cos = tan = 5 4545 -3 5 -4 3

13 Example: Let (-4,-6) be a point on the terminal side of (in standard position). Determine the sine, cosine, tangent, cosecant, secant and cotangent of. Step 1: Draw a picture of the situation. (-4,-6) Step2: Draw the reference triangle (drop the altitude to the x-axis). Then determine the lengths of the sides of the reference triangle. 6 4 Determine the radius of the circle passing through the point referenced. Step 3: Use the non-unit circle definitions to determine the values of the trig. functions requested. sin = cos = tan = csc =sec = cot = 213 -313 13 -213 13 3232 -13 3 -13 2 2323

14 (+,+) (,+) (,) (+,) All Star Trig. Class


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