- Definitions of many-to-one and one-to-one functions
- Unit circle
- Sine, Cap-Sine, Arcsin!
- Cosine, Cap-Cosine, Arccos!
- Tangent, Cap-Tangent, Arctan!
- Using Right Triangles

- Review of grade 12 precalculus (unit circle unit)
- Ask yourself what angle you're looking for and imagine the unit circle
- We gave the answers to the above questions, but Mr.K then says that one of the solutions in each answer is wrong, but why?
- Introducing the inverses of the trigonometric functions!

SLIDE 3: VOILA! THE UNIT CIRCLE!

SLIDE 4: SINE! CAP SINE! ARCSIN!

- We have the sine function. We want to know its inverse, but we can't since it's a many-to-one function.
- If we restrict the domain of the sine function to [-pi/2, pi/2], we have a function that has the same range as the sine function. This restricted sine function is the Sine (pronounced "Cap-Sine") function.
- Take the inverse of Sine (switch the x- and y-coordinates). We get the arcsine function.
- Note that Sine takes up Quadrants I and IV of sine. Thus, only values of sine found in QI and QIV are in the domain of Sine.

SLIDE 5: COSINE! CAP COSINE! ARCCOS!

- We have the cosine function. We want to know its inverse, but we can't since it's a many-to-one function.
- If we restrict the domain of the cosine function to [0, pi], we have a function that has the same range as the cosine function. This restricted cosine function is the Cosine (pronounced "Cap-Cosine") function.
- Take the inverse of cosine (switch the x- and y-coordinates). We get the arcsine function.
- Note that Cosine takes up Quadrants I and II of cosine. Thus, only values of cosine found in QI and QII are in the domain of Cosine.

SLIDE 6: TANGENT! CAP TAN! ARCTAN!

- We have the tangent function. We want to know its inverse, but we can't since it's a many-to-one function.
- If we restrict the domain of the tangent function to [-pi/2, pi/2], we have a function that has the same range as the tangent function. This restricted cosine function is the Tangent (pronounced "Cap-Tangent") function.
- Take the inverse of tangent (switch the x- and y-coordinates). We get the arctan function.
- Note that Cosine takes up Quadrants I and IV of tangent. Thus, only values of tangent found in QI and QIV are in the domain of Tangent.

SLIDE 7 TO 12: A BARRAGE OF QUESTIONS!

- We found the values of each using the unit circle. Note that some values of the unit circle aren't in the domain of the "Cap functions."

- 3a and 3b are undefined because the angle doesn't live in the domain of Sine and Cos.

- Sine and sine, Cosine and cosine, and Tangent and tangent are inverses of each other. Thus, they undo each other, like multiplying a number by 3 then dividing the number by 3.

SLIDE 13: USING RIGHT TRIANGLES!

- In 8a, we let sin^-1 2/3 = x to make a simplified expression cot x. Looks easier to solve, right? We used the definition of sine (the ratio of opposite side to the hypotenuse side) to determine what cot x is. We solved for cot x.

HOUSEKEEPING:

- Next scribe is Kristina.
- And don't forget to listen to the Dr. Love messages during the last ten minutes of class!

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