Notes – Trigonometry



Introduction to Trigonometry

The field of mathematics called “Trigonometry” is the study of right triangles.

Key word: SOH CAH TOA or [pic] [pic] [pic]

[pic] [pic] [pic]

S: sine (sin) O: opposite leg

C: cosine (cos) A: adjacent leg

T: tangent (tan) H: hypotenuse

The three sides of the triangles are referred to as Hypotenuse (H), Adjacent (A), and Opposite (O). Label each side of each triangle using angle W as your reference.

Use the triangle at the right to determine the following values.

sin 40° = sin 50° =

cos 40° = cos 50° =

tan 40° = tan 50º =

Write each ratio in simplest form.

1. sin A 2. cos A 3. tan A

4. sin B 5. cos B 6. tan B

In right triangle HLK, name the ratio represented for the given angle.

7. [pic] 8. [pic] 9. [pic]

10. [pic] 11. [pic] 12. [pic]

Using special right triangles to write each trigonometric ratio as a fraction.

13. tan 60º 14. sin 45º 15. cos 30º 16. tan 45º 17. cos 60º

18. sin 60º 19. cos 45º 20. tan 30º 21. sin 30º

More Trigonometric Ratios

The cosine, sine and tangent ratios are defined in terms of the lengths of the sides of a right triangle. Three other ratios are the secant, the cosecant and the cotangent ratios. The ratios are abbreviated as sec, csc, cot.

sec A = [pic]

csc A = [pic]

cot A = [pic]

The secant ratio for [pic]A is the reciprocal of its ___________ratio.

The cosecant ratio for [pic]A is the reciprocal of its _______ratio.

The cotangent ratio for [pic]A if the reciprocal of its _________ratio.

Write each ratio in simplest form.

22. sec A 23. csc A 24. cot A

25. sec B 26. csc B 27. cot B

In right triangle HLK, name the ratio represented for the given angle.

28. [pic] 29. [pic] 30. [pic]

31. [pic] 32. [pic] 33. [pic]

-----------------------

[pic]

[pic]

m

[pic]

[pic]

p

n

40º

50º

W

W

Y

Y

Z

Z

[pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download