14 Mid-Chapter Quiz

Do you know HOW?

Verify each identity.

1. sin θ tan θ = sec θ − cos θ sine theta tangent theta equals secant theta negative cosine theta
2. tan θ = sec θ csc θ tangent theta equals . fraction secant theta , over co-secant theta end fraction
3. sec θ cos θ = 1 + tan 2 θ fraction secant theta , over cosine theta end fraction . equals 1 plus , tangent squared , theta
4. cos θ sec θ = 1 − sin θ csc θ fraction cosine theta , over secant theta end fraction . equals 1 minus . fraction sine theta , over co-secant theta end fraction

Simplify each trigonometric expression.

5. sec θ cot θ secant theta co-tangent theta
6. sec 2 θ − 1 secant squared , theta negative 1
7. − 1 − cot 2 θ negative 1 minus , co-tangent squared , theta
8. sin θ cot θ sine theta co-tangent theta
9. 1 − cos 2 θ 1 minus , cosine squared , theta
10. sec θ sin θ tan θ fraction secant theta sine theta , over tangent theta end fraction
11. cos θ tan θ cosine theta tangent theta
12. sin θ + cos θ cot θ sine theta plus cosine theta co-tangent theta

Use a unit circle and a 30 ° − 60 ° − 90 ° 30 degrees negative 60 degrees negative 90 degrees triangle to find the degree measures of the angles.

13. angles whose cosecant is 2
14. angles whose secant is − 2 negative 2
15. angles whose tangent is 3 square root of 3
16. angles whose cotangent is − 3 negative square root of 3

Find the value of each expression in radians to the nearest thousandth. If the expression is undefined, write Undefined.

17. cos − 1 ( − π 5 ) cosine super negative 1 end super . open , negative , pi over 5 , close
18. sin − 1 π 10 sine super negative 1 end super . pi over 10
19. tan − 1 4.35 tangent super negative 1 end super . 4.35
20. cos − 1 ( − 2.35 ) cosine super negative 1 end super . open negative , 2.35 , close
21. sin − 1 ( − 5 π 7 ) sine super negative 1 end super . open . negative , fraction 5 pi , over 7 end fraction . close
22. tan − 1 ( − 1.05 ) tangent super negative 1 end super . open negative , 1.05 , close
23. tan − 1 π 9 tangent super negative 1 end super . pi over 9
24. sin − 1 ( − 0.45 ) sine super negative 1 end super . open negative , 0.45 , close

Solve each equation for θ theta with 0 ≤ θ < 2 π . 0 less than or equal to theta less than 2 pi .

25. 2 cos θ = − 2 2 cosine theta equals negative square root of 2
26. sin θ ( cos θ + 1 ) = 0 sine theta open cosine theta plus 1 close equals 0
27. tan 2 θ − 3 tan θ = 0 tangent squared , theta negative square root of 3 tangent theta equals 0

In Δ ABC , ∠ cap delta C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.

28. b = 14 , c = 16 b equals 14 comma c equals 16
29. a = 7.9 eh equals 7.9 , b = 6.2 b equals 6.2
30. b = 29 , c = 35 b equals 29 comma c equals 35
31. a = 6.1 eh equals 6.1 , c = 10.2 c equals , 10.2
32. a = 10 , c = 14 eh equals 10 comma c equals 14
33. a = 9 , b = 4 eh equals 9 comma b equals 4
34. b = 7 , c = 12 b equals 7 comma c equals 12
35. b = 11.1 b equals , 11.1 , c = 26.3 c equals , 26.3

Sketch a right triangle with θ theta as the measure of one acute angle. Find the other five trigonometric ratios of θ . theta .

36. sin θ = 5 7 sine theta equals , 5 sevenths
37. cos θ = 2 9 cosine theta equals , 2 ninths
38. sec θ = 20 11 secant theta equals , 20 over 11
39. csc θ = 8 3 co-secant theta equals , 8 thirds
40. tan θ = 11 4 tangent theta equals , 11 over 4
41. cot θ = 5 co-tangent theta equals 5

Do you UNDERSTAND?

42. Writing How is solving the trigonometric equation tan 2 θ − 3 tan θ + 2 = 0 tangent squared , theta negative 3 tangent theta plus 2 equals 0 similar to solving x 2 − 3 x + 2 = 0 ? x squared , minus 3 x plus 2 equals 0 question mark
43. Open-Ended Draw a right triangle. Measure the lengths of two sides, and then find the length of the remaining side without measuring.
44. Reasoning Explain why the trigonometric equation sin 2 θ − sin θ − 6 = 0 sine squared , theta negative sine theta negative 6 equals 0 has no solutions.
45. Indirect Measure A man stands at the top of a building and you are standing 45 feet from the building. The angle of elevation to the top of the man's head is 54 ° , 54 degrees comma and the angle of elevation to the man's feet is 51 ° . 51 degrees . To the nearest inch, how tall is that man?

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