1. Part I Finding Values for Trig Functions
Sin = opposite ÷ hypotenuse
Cos = adjacent ÷ hypotenuse
Tan = opposite ÷ adjacent
Opposite
Hypotenuse θ
Adjacent
Tim Glahn LCJVS Mathematics Dept.

2. θ
13 in
5 in
12 in
Find cos <θ =
Tim Glahn LCJVS Mathematics Dept.

3. θ
13 in
5 in
12 in
Find sin <θ =
Tim Glahn LCJVS Mathematics Dept.

4. θ
13 in
5 in
12 in
Find tan <θ =
Tim Glahn LCJVS Mathematics Dept.

5. Practice
Tim Glahn LCJVS Mathematics Dept.

6. Remember……. θ Hypotenuse Opposite Adjacent
Tim Glahn LCJVS Mathematics Dept.

7. Find the sin <α 20 in 12in 15 in <β <α
Tim Glahn LCJVS Mathematics Dept.

8. Find the cos <β 13 in 12in 5 in <β <α
Tim Glahn LCJVS Mathematics Dept.

9. Find the sin <α 13 in 12in 5 in <β <α
Tim Glahn LCJVS Mathematics Dept.

10. Find the sin <β <β 20 in 12in <α 15 in
Tim Glahn LCJVS Mathematics Dept.

11. Find the tan <α <β 13 in 12in <α 5 in
Tim Glahn LCJVS Mathematics Dept.

12. Find the tan <β <β 20 in 12in <α 15 in
Tim Glahn LCJVS Mathematics Dept.

13. Find the cos <α <β 13 in 12in <α 5 in
Tim Glahn LCJVS Mathematics Dept.

14. Find the tan <β <β 17 in 16in <α 5 in
Tim Glahn LCJVS Mathematics Dept.

15. Find the tan <β <β 13 in 12in <α 5 in
Tim Glahn LCJVS Mathematics Dept.

16. Find the cos <α <β 20 in 12in <α 15 in
Tim Glahn LCJVS Mathematics Dept.

17. Find the cos <α <β 13 in 12in <α 5 in
Tim Glahn LCJVS Mathematics Dept.

18. Find the sin <β <β 13 in 12in <α 5 in
Tim Glahn LCJVS Mathematics Dept.

19. Find the tan <α <β 13 in 12in <α 5 in
Tim Glahn LCJVS Mathematics Dept.

20. Find the tan <α <β 20 in 12in <α 15 in
Tim Glahn LCJVS Mathematics Dept.

21. Find the tan <β <β 20 in 12in <α 15 in
Tim Glahn LCJVS Mathematics Dept.

22. Find the sin <α 16in 5 in <β 17 in <α
Tim Glahn LCJVS Mathematics Dept.

23. Find the cos <β <β 17 in 16in <α 5 in
Tim Glahn LCJVS Mathematics Dept.

24. Find the sin <β <β 17 in 16in <α 5 in
Tim Glahn LCJVS Mathematics Dept.

25. Find the cos <β <β 20 in 12in <α 15 in
Tim Glahn LCJVS Mathematics Dept.

26. Part II Finding Angles Using Trig Functions
Use the arc sin, arc cos, and arc tan functions to find angles.
Sin-1 Cos-1 and Tan-1 are how they appear on your Calculator
Any two sides can be used to find an angle measure.
Tim Glahn LCJVS Mathematics Dept.

27. Which Arc Function Do I Use?
If you have opposite and hypotenuse use the arc sin or sin-1.
If you have adjacent and hypotenuse use the arc cos or cos-1
If you have opposite and adjacent use the arc tan or tan-1
Tim Glahn LCJVS Mathematics Dept.

28. Finding an Angle Use Sin-1 θ = Sin-1(15/31) = 28º56’ 31 15 θ
hypotenuse 31 15
Opposite θ
Use Sin-1
θ = Sin-1(15/31)
= 28º56’
Tim Glahn LCJVS Mathematics Dept.

29. Use Cos-1 θ = Cos-1(22/31) = 44º 47’ 31 θ 22 hypotenuse Adjacent
Tim Glahn LCJVS Mathematics Dept.

30. Use Tan-1 θ = Tan-1(15/22) = 34º17’ 15 θ 22 Opposite Adjacent
Tim Glahn LCJVS Mathematics Dept.