1. Right Triangle Trigonometry Integrated Math 4 Mrs. Tyrpak

2. Opposite Adjacent

3. Example #1

4. Example #2 Find the exact value of sin(45), cos(45), and tan(45).

5. Example #3 Use an equilateral triangle to find the exact values of sin(60), cos(60), sin(30), cos(30).

6. Special Angles sin(30)= cos(30)= tan(30)= sin(45)= cos(45)= tan(45)= sin(60)= cos(60)= tan(60)=

7. Co-functions of complementary angles are equal sin(90 – x)= cosxcos(90 -x) = sinx tan(90 – x)= cotxcot(90 -x) = tanx sec(90 – x)= cscxcsc(90-x) = secx

8. Applications of Right Triangles Angle of elevation: the angle from the horizontal UPWARD to the object Angle of depression: the angle from the horizontal DOWNWARD to the object

9. Example #4 A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5 degrees. How tall is the tree?

10. Example #5 From a 60-foot observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angle of depression of the boat is 4.5 degrees. How far is the boat from the shoreline?

11. Reciprocal Identities

12. Reasoning with Reciprocal Functions

14. Thanks for your hard work! Don’t forget to complete both the extension and enrichment assignments before you move on. Remember to take a short break if you feel stuck. It will help clear your head and help you focus!