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Problem 41
Find a calculator approximation to four decimal places for each circular function value. See Example 3.
sec 2.8440
Problem 43
Find a calculator approximation to four decimal places for each circular function value. See Example 3.
cot 6.0301
Problem 55
Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)
cos 2
Problem 56
Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)
sin ( ―1)
Problem 57
Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)
sin 5
Problem 58
Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)
cos 6
Problem 59
Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)
tan 6.29
Problem 61
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
tan s = 0.2126
Problem 62
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
cos s = 0.7826
Problem 63
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
sin s = 0.9918
Problem 65
Find the approximate value of s, to four decimal places, in the interval [0 , π/2] that makes each statement true.
sec s = 1.0806
Problem 67
Find the exact value of s in the given interval that has the given circular function value.
[π/2, π] ; sin s = 1/2
Problem 69
Find the exact value of s in the given interval that has the given circular function value.
[π, 3π/2] ; tan s = √3
Problem 71
Find the exact value of s in the given interval that has the given circular function value.
[3π/2, 2π] ; tan s = -1
Problem 73
Find the exact values of s in the given interval that satisfy the given condition.
[0, 2π) ; sin s = -√3 / 2
Problem 75
Find the exact values of s in the given interval that satisfy the given condition.
[0 , 2π) ; cos² s = 1/2
Problem 77
Find the exact values of s in the given interval that satisfy the given condition.
[-2π , π) ; 3 tan² s = 1
Problem 79
Suppose an arc of length s lies on the unit circle x² + y² = 1, starting at the point (1, 0) and terminating at the point (x, y). (See Figure 12, repeated below.) Use a calculator to find the approximate coordinates for (x, y) to four decimal places.
s = 2.5
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Problem 81
Suppose an arc of length s lies on the unit circle x² + y² = 1, starting at the point (1, 0) and terminating at the point (x, y). (See Figure 12, repeated below.) Use a calculator to find the approximate coordinates for (x, y) to four decimal places.
s = ―7.4
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Problem 83
For each value of s, use a calculator to find sin s and cos s, and then use the results to decide in which quadrant an angle of s radians lies.
s = 51
Problem 85
For each value of s, use a calculator to find sin s and cos s, and then use the results to decide in which quadrant an angle of s radians lies.
s = 65
Problem 3.37
Find the angular speed ω for each of the following.
a wind turbine with blades turning at a rate of 15 revolutions per minute
Problem 3.43
Find the linear speed v for each of the following.
the tip of a propeller 3 m long, rotating 500 times per min (Hint: r = 1.5 m)
Problem 3.53
A thread is being pulled off a spool at the rate of 59.4 cm per sec. Find the radius of the spool if it makes 152 revolutions per min.
Problem 3.45
Find the linear speed v for each of the following.
a point on the equator moving due to Earth's rotation, if the radius is 3960 mi
Problem 3.39
Find the linear speed v for each of the following.
the tip of the minute hand of a clock, if the hand is 7 cm long
Problem 3.41
Find the linear speed v for each of the following.
a point on the edge of a flywheel of radius 2 m, rotating 42 times per min
Problem 3.55
The propeller of a 90-horsepower outboard motor at full throttle rotates at exactly 5000 revolutions per min. Find the angular speed of the propeller in radians per second.
Problem 11
Use the formula ω = θ/t to find the value of the missing variable.
ω = 2π/3 radians per sec, t = 3 sec
Problem 13
Use the formula ω = θ/t to find the value of the missing variable.
ω = 0.91 radian per min, t = 8.1 min