1. TRIGONOMETRY Find trigonometric ratios using right triangles Solve problems using trigonometric ratios Sextant

2. TRIGONOMETRIC RATIOS TRIGONOMETRY comes from two Greek terms: – trigon, meaning triangle – metron, meaning measure TRIGONOMETRY comes from two Greek terms: – trigon, meaning triangle – metron, meaning measure

3. TRIGONOMETRIC RATIOS TRIGONOMETRY comes from two Greek terms: – trigon, meaning triangle – metron, meaning measure TRIGONOMETRY comes from two Greek terms: – trigon, meaning triangle – metron, meaning measure A ratio of the lengths of sides of a right triangle is called a TRIGONOMETRIC RATIO.

4. TRIGONOMETRIC RATIOS The three most common trigonometric ratios are: Sine Cosine Tangent

5. Key ConceptTrigonometric Ratios hypotenuse A B C Begin with a right triangle

6. Key ConceptTrigonometric Ratios sine of  A = measure of leg opposite  A measure of hypotenuse hypotenuse leg opposite  A leg opposite  B A B C

7. Key ConceptTrigonometric Ratios sine of  A = measure of leg opposite  A measure of hypotenuse hypotenuse leg opposite  A leg opposite  B A B C sin A = BC AB

8. Key ConceptTrigonometric Ratios sine of  A = measure of leg opposite  A measure of hypotenuse hypotenuse leg opposite  A leg opposite  B A B C sin A = BC AB sine of  B = measure of leg opposite  B measure of hypotenuse

9. Key ConceptTrigonometric Ratios sine of  A = measure of leg opposite  A measure of hypotenuse hypotenuse leg opposite  A leg opposite  B A B C sin A = BC AB sine of  B = measure of leg opposite  B measure of hypotenuse sin B = AC AB

10. Key ConceptTrigonometric Ratios cosine of  A = measure of leg adjacent to  A measure of hypotenuse hypotenuse leg adjacent to  A A B C

11. Key ConceptTrigonometric Ratios cosine of  A = measure of leg adjacent to  A measure of hypotenuse hypotenuse leg adjacent to  A A B C cos A = AC AB

12. Key ConceptTrigonometric Ratios cosine of  A = measure of leg adjacent to  A measure of hypotenuse hypotenuse leg adjacent to  B leg adjacent to  A A B C cos A = AC AB cosine of  B = measure of leg adjacent to  B measure of hypotenuse

13. Key ConceptTrigonometric Ratios cosine of  A = measure of leg adjacent to  A measure of hypotenuse hypotenuse leg adjacent to  B leg adjacent to  A A B C cos A = AC AB cosine of  B = measure of leg adjacent to  B measure of hypotenuse cos B = BC AB

14. Key ConceptTrigonometric Ratios tangent of  A = measure of leg opposite  A measure of leg adjacent to  A hypotenuse leg opposite  A and adjacent to  B leg adjacent to  A and opposite  B A B C

15. Key ConceptTrigonometric Ratios tangent of  A = measure of leg opposite  A measure of leg adjacent to  A hypotenuse leg opposite  A and adjacent to  B leg adjacent to  A and opposite  B A B C tan A = BC AC

16. Key ConceptTrigonometric Ratios tangent of  A = measure of leg opposite  A measure of leg adjacent to  A hypotenuse leg opposite  A and adjacent to  B leg adjacent to  A and opposite  B A B C tan A = BC AC tangent of  B = measure of leg opposite  B measure of leg adjacent to  B

17. Key ConceptTrigonometric Ratios tangent of  A = measure of leg opposite  A measure of leg adjacent to  A hypotenuse leg opposite  A and adjacent to  B leg adjacent to  A and opposite  B A B C tan A = BC AC tangent of  B = measure of leg opposite  B measure of leg adjacent to  B tan B = AC BC

18. Reading Math SOH – CAH – TOA sin A = cos A = tan A = opp hyp adj hyp opp adj

19. TRIGONOMETRIC RATIOS The three most common trigonometric ratios are: Sine Cosine Tangent Sine function key Cosine function key Tangent function key