## Reflection: Vertical Alignment Using Trigonometry to Solve Right Triangles - Section 1: Learning the Decision-Making Framework

If I had to pick one concept that is central to high school mathematics, it is the concept of functions. I'll admit that when I went through high school, I had no idea what a function was apart from it having something to do with f(x) and the notation never did sit quite right with me.

I'd have to say that students tend to be just as confused when it comes to functions, particularly trigonometric functions, especially the inverse trig functions. So in this lesson, I really try to make connections to the concept of functions.

For any function, I like for my students to be able to tell me what its "purpose" is. I would want them to know that sine, cosine and tangent are functions that "take" an angle measure as the input and "return" a ratio as the output. Once they understand this, they'll be less likely to think that sin50 means sine times 50, for example.

Next I want them to understand that the inverse of a function takes what would be the output of the function and returns the input that would have produced it. So the inverses of sine, cosine and tangent take ratios as their inputs and return angle measures as their outputs. When students begin to understand this, then they'll be more clear on when they should use sine, for example, and when they should use "sine to the negative first power"...JUST KIDDING.

So again, building students' literacy around functions is a long term process that hopefully is occurring throughout the entire four years of high school.

Building Knowledge of Functions: Inverses
Vertical Alignment: Building Knowledge of Functions: Inverses

# Using Trigonometry to Solve Right Triangles

Unit 7: Right Triangles and Trigonometry
Lesson 3 of 6

## Big Idea: Elevate your mind...at an angle of arctan(opposite/adjacent)....By the end of this lesson, students will know why this makes no sense.

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60 minutes

### Anthony Carruthers

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