Lesson 5 Maintaining Your Identity Solidify Understanding

Ready

In the diagram, triangle is a right triangle.

  • Point is any point on the circle and is described by the rectangular coordinates .

  • is the length of the arc subtended by angle .

  • is the radius of circle .

Circle with Triangle ABC with hypotenuse AB=r, BC=y, and AC=x with angle theta = angle A and arc s.

1.

is described by .

a.

Find .

b.

Find to the nearest thousandth of a radian. ( decimal places)

c.

Find by using the formula .

d.

Describe point using the coordinates .

e.

Describe point using the radius and arc length .

2.

is described by .

a.

Find .

b.

Find to the nearest thousandth of a radian. ( decimal places)

c.

Find by using the formula .

d.

Describe point using the coordinates .

e.

Describe point B using the radius and arc length .

3.

is described by .

a.

Find .

b.

Find to the nearest thousandth of a radian. ( decimal places).

c.

Find by using the formula .

d.

Describe point using the coordinates .

e.

Describe point using the radius and arc length .

4.

is described by .

a.

Find .

b.

Find to the nearest thousandth of a radian. ( decimal places).

c.

Find by using the formula .

d.

Describe point using the coordinates .

e.

Describe point using the radius and arc length .

Set

The Cofunction identity states: and .

Complete the statements, using the Cofunction identity.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

Let .

a.

Use the Pythagorean identity to find the value of , given .

b.

Use the Quotient identity , the given information, and your answer in part (a) to calculate the value of .

15.

Let .

a.

Find given: .

b.

Find .

c.

Find .

16.

Write in a different form to see if the given identity is true.

17.

Perform the indicated multiplication to see if you can get the Pythagorean Identity.

18.

Use your work in problem #17 to prove .

19.

Rearrange the terms in this equation until you get the Pythagorean Identity.

Go

Find two solutions in degrees and two solutions in radians for each equation. and . Do NOT use a calculator.

20.

degrees:

radians:

21.

degrees:

radians:

22.

degrees:

radians:

23.

degrees:

radians:

24.

degrees:

radians:

25.

degrees:

radians: