I/D1: Unit N

How do SRT and UC relate?

Inquiry Activity Summary:
In this activity we were asked to find and simplify the lengths of the special right triangles with the hypotenuse equalling 1. We must always draw the fortunate plane for each because the coordinate is derived from the unit circle.

30-60-90 SRT

Here we have the special right triangle of 30-60-90. This triangle has an original hypotenuse of (2x) a height of (x) and the length of (x rad 3). To make the hypotenuse of (2x) to equal 1 we must divide all sides of the triangle by (2x).

We divided all sides by 2x to reduce the hypotenuse equal to 1. The effect of doing this cause the length of the triangle to become rad 3/2. The height then becomes 1/2.

45-45-90 SRT

In this special right triangle we have the 45-45-90. The rules for this triangle we have the hypotenuse equal x rad 2 and both the height and length equal x.

To make the hypotenuse equal 1 we have to divide it by x rad 2. And whatever we do to one side we must do to all to keep it proportional. When we do this the height and length become rad 2/2.

60-30-90 SRT

This triangle is similar to the 30-60-90 triangle but it is in a different position. The hypotenuse is 2x the length is x and the height is x rad 3. We must do what we did to the first triangle and divide the sides by 2x.

When we divide by 2x the hypotenuse becomes 1, the length becomes 1/2, and the height is rad 3/2.

How does this activity help you to derive the Unit Circle?

This activity helps derive the unit circle because it helps us understand and know where the points of the unit circle come from. This activity also showed the way the triangles are proportioned so the hypotenuse is equal to one. 

5. 

The quadrants of the triangles shown are in quadrant one. The quadrants change the value of it is either positive or negative. In quadrant 2 x is negative and y is positive, in quadrant 3 x and y are negative, quadrant 4 x is positive and y is negative.

This triangle is in quadrant 2 and all x-values are negative.

In this it shows a triangle in quadrant and all values are negative.

This triangle is located in quadrant and all y values are negative in this quadrant.

INQUIRY ACTIVITY REFLECTION

The coolest thing I learned from this activity was that these triangles are the only ones that have these special rules.

This activity will help me in this unit because it will help me understand the unit circle and how the quadrants can affect the triangle and which points are positive and negative.

Something I never realized before about special right triangles and the unit circle is that the quadrant affects the negative and positive of a point. And that the triangles have special rules that only apply to these specific triangles.