Trigonometric Ratios-Mathematics K-12 Curriculum.pptx

Six Trigonometric Ratios

1. The Six Trigonometric Ratios

2. Learning competencies : Illustrates the six trigonometric ratios: sine, cosine, tangent, secant, cosecant, and cotangent. Use trigonometric ratios to solve real-life problems involving right triangles.

3. TRIGONOMETRY

4. Trigonometry is a branch of mathematics that deals with the relation between the sides and the angles of triangles . It also deals with measurements based on these sides and angles. Greek words: trigonon which means triangle metria which means measurement

5. Angles An angle is a geometric figure formed by rotating a half line about its endpoint from its initial position to its terminal position. The endpoint of the half line is called the vertex . The initial position of the half line is called the initial side of the angle, and the terminal position of the half line is called the terminal side of the angle.

6. Kinds of Angles Acute angle- an angle whose measurement is between 0˚ and 90˚. Obtuse angle- an angle whose measurement is between 90˚ and 180˚ . Right angle- an angle whose measurement is exactly 90˚. Straight angle- an angle whose measurement is exactly 180˚. Reflex angle- an angle whose measurement is between 180˚ and 360˚. Complementary angle- two angles whose sum is 90˚. Supplementary angle- two angles whose sum is 180˚.

7. The Six Trigonometric Functions

8. The six trigonometric functions are sine , cosine , tangent , cotangent , cosecant and secant .

9. The Six Trigonometric Ratios Trigonometric Function Abbreviation Sine Sin Cosine Cos Tangent Tan Cotangent Cot Cosecant Csc Secant Sec

10. Six Trigonometric Ratios Sin θ = Opposite Hypotenuse Cos θ = Adjacent Hypotenuse Tan θ = Opposite Adjacent Cot θ = Adjacent Opposite Sec θ = Hypotenuse Opposite Csc θ = Hypotenuse Opposite

11. Hypotenuse θ Adjacent Opposite Parts of a Right Triangle The three sides of the right triangle are: Hypotenuse (the longest side) Perpendicular (opposite side to the angle) Base (Adjacent side of the angle)

12. Example 45˚ 5 cm ? ?

13. Solve: 75˚ 9 cm hypotenuse Find: 2. adjacent

14. Assessment: Answer the following. 1. A ladder leans against the brick wall. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 ft. on the wall. Find the angle the ladder makes with the wall. 2. A nursery plants a new tree and attaches a guy wire to help support the tree while its roots takes hold. An 8 ft. wire is attached to the tree and to a stake in the ground. The stake in the ground makes a 42˚ angle to the tree. Find the height of the connection point on the tree.

15. Assignment From the top of a cliff 250 ft. high, the angle of depression of a boat is 10˚. How far out is the boat to the cliff?