Chapter 4 Trigonometric Functions
Chapter 4 Trigonometric Functions
Chapter 4 Trigonometric Functions
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<strong>Trigonometric</strong> <strong>Functions</strong><br />
49. f ( θ) = 2cosθ − cos2θ<br />
⎛π ⎞ π ⎛ π ⎞<br />
f ⎜ 2cos cos 2<br />
6<br />
⎟= −<br />
6<br />
⎜ ⋅<br />
6<br />
⎟<br />
⎝ ⎠ ⎝ ⎠<br />
⎛ 3 ⎞ ⎛π<br />
⎞<br />
= 2 −cos<br />
⎜<br />
2 ⎟ ⎜<br />
3<br />
⎟<br />
⎝ ⎠ ⎝ ⎠<br />
2 3 1<br />
= −<br />
2 2<br />
2 3 −1<br />
=<br />
2<br />
θ<br />
50. f ( θ) = 2sinθ<br />
− sin 2<br />
π<br />
⎛π<br />
⎞ π<br />
3<br />
f ⎜ 2sin sin<br />
3<br />
⎟ = −<br />
⎝ ⎠ 3 2<br />
⎛ 3 ⎞ ⎛π<br />
⎞<br />
= 2 −sin<br />
⎜<br />
2 ⎟ ⎜<br />
6<br />
⎟<br />
⎝ ⎠ ⎝ ⎠<br />
2 3 1<br />
= −<br />
2 2<br />
2 3 −1<br />
=<br />
2<br />
51.<br />
52.<br />
⎛<br />
1<br />
tan<br />
π ⎞<br />
⎜ − θ = cot θ =<br />
2<br />
⎟<br />
⎝ ⎠ 4<br />
⎛π<br />
⎞ 1 1<br />
csc⎜<br />
− θ secθ<br />
3<br />
2<br />
⎟= = = =<br />
⎝ ⎠ cosθ<br />
1<br />
3<br />
a<br />
53. tan 40°=<br />
630<br />
a = 630 tan 40°<br />
a ≈630(0.8391) ≈529<br />
The distance across the lake is approximately 529 yards.<br />
h<br />
54. tan 40°=<br />
35<br />
h = 35tan 40°<br />
h ≈35(0.8391) ≈ 29<br />
The tree’s height is approximately 29 feet.<br />
55.<br />
125<br />
tanθ =<br />
172<br />
Use a calculator in degree mode to find θ .<br />
Many Scientific Calculators<br />
125 ÷ 172 = TAN −1<br />
Many Graphing Calculators<br />
−1<br />
TAN ( 125 ÷ 172 ) ENTER<br />
The display should show approximately 36. Thus, the angle of elevation of the sun is approximately 36°.<br />
514<br />
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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