Chapter 4 Trigonometric Functions

Trigonometric Functions
69.
θ 0.4 0.3 0.2 0.1 0.01 0.001 0.0001 0.00001
cosθ 0.92106 0.95534 0.98007 0.99500 0.99995 0.9999995 0.999999995 1
cosθ
− 1 –0.19735 –0.148878 –0.099667 –0.04996 –0.005 –0.0005 –0.00005 0
θ
cosθ
−1
approaches 0 as θ approaches 0.
θ
70. does not make sense; Explanations will vary. Sample explanation: An increase in the size of a triangle does not affect
the ratios of the sides.
71. does not make sense; Explanations will vary. Sample explanation: This value is irrational. Irrational numbers are
rounded on calculators.
72. does not make sense; Explanations will vary. Sample explanation: The sine and cosine are cofunctions of each other.
The sine and cosine are not reciprocals of each other.
73. makes sense
74. false; Changes to make the statement true will vary. A sample change is:
tan 45 ° ⎛45
tan
° ⎞
≠ ⎜ ⎟
tan15° ⎝15°
⎠
75. true
76. false; Changes to make the statement true will vary. A sample change is:
1 1 2
sin 45°+ cos 45°= + = ≠ 1
2 2 2
77. true
78. In a right triangle, the hypotenuse is greater than either other side. Therefore both
less than 1 for an acute angle in a right triangle.
opposite
hypotenuse
and
adjacent
hypotenuse
must be
79. Use a calculator in degree mode to generate the following table. Then use the table to describe what happens to the
tangent of an acute angle as the angle gets close to 90°.
θ 60 70 80 89 89.9 89.99 89.999 89.9999
tanθ 1.7321 2.7475 5.6713 57 573 5730 57,296 572,958
As θ approaches 90°, tanθ increases without bound. At 90°, tanθ is undefined.
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