1. 2a Basic Trigonometric Functions Sine, Cosine, and tangent

2. What is Trigonometry?
The study of how the angles and sides of a triangle are related
Basic Trigonometry deals mainly with Right Triangles
There are three basic trigonometry functions Sine, Cosine, and Tangent
These trig. Functions uses the ratios of each side to find the angles in a right triangle

3. II) Naming Sides of a Right Triangle
When naming the sides of a R.T., they are relative to the angle that you are using
Hypotenuse
Opposite Side
Adjacent Side
Hypotenuse
Adjacent Side
Opposite Side
Note: The Adjacent and Opposite side can be switched around depending on which angle you use.
Note: The Hypotenuse must be the longest side and opposite from the “box”

4. III) Tangent Ratio
The tangent ratio is used when you are given the “Opposite” and “Adjacent” sides of a R.T.
Your calculator must be in “Deg” mode (Degree)
The angle doesn’t change when you have a larger similar triangle because the RATIO stays the same
Measure the angle:
When you “Tan” the angle, it will
be equal to the RATIO of the opposite side divided by the
adjacent side

5. What is Sine and Cosine? Sine Function
Sine & Cosine are Trigonometric Functions
Right Triangles
When you Sine an angle, it will give you the RATIO of the Opposite side over the Hypotenuse
When you Cosine an angle, it will give you the RATIO of the Adjacent side over the Hypotenuse
Hypotenuse
Hypotenuse
Opposite Side
Adjacent Side
Sine Function
Cosine Function

6. II) Sine Ratio
The Sine ratio is used when you are given the “Opposite” side and “Hypotenuse” of a R.T.
“Deg” mode (Degree)
Measure the angle:
When you “Sin” the angle, it will
be equal to the RATIO of the Opposite side divided by the
Hypotenuse

7. III) Cosine Ratio
The Cosine ratio is used when you are given the “Adjacent” side and “Hypotenuse” of a R.T.
Measure the angle:
When you “Cos” the angle, it will
be equal to the RATIO of the Adjacent side divided by the
Hypotenuse

8. How to Use the Tangent Function
The tangent function is equal to the Opposite side divided by the adjacent side
Angle
Ratio
The tangent function can be used to find missing sides when an angle is given

9. SOH-CAH-TOA
The Trig. Function used should depend on which sides of a R.T. you are given
SOH-CAH-TOA

10. Ex: Find the missing sides to 2 decimal places using Tangent
Cross Multiply!

11. Ex: Find the missing sides to 2 decimal places
Cross Multiply!

12. Ex: Find the missing sides to 2 decimal places
Cross Multiply!

13. Q: Given each of the following values below, which of the following can sinθ not be equal to?

14. IV) Finding Angles Using Tan. Function
When finding angles, use the tan-1(x)
The tan-1(x) of a ratio will give you the angle

15. IV) Finding Angles with Inverse Sine & Inverse Cosine
When finding angles, use the sin-1(x) or cos-1(x)
The inverse function of a ratio will give you the angle

16. Practice: Find the missing angle to the nearest degree

17. Practice: Find the missing angle to the nearest degree

18. Challenge: Two building are 70meters apart
Challenge: Two building are 70meters apart. The shorter building is 50m high. A cable is attached to both building. The angle of inclination is 15°. How tall is the taller building?

19. Homework:
Assignment 2a