25. A Ferris wheel has a radius of 20 meters and its center is located 28 meters above the ground. If a passenger gets on the Ferris wheel at the 3 o'clock position and the wheel rotates counterclockwise at a rate of one full rotation every 5 minutes, write an equation for the height of the passenger above the ground as a function of time in seconds.
Answer: h(t) = 48 + 20sin((t/300)pi)
how to get the answers:
which represents the reference angle for 3pi/4
The answer is pi/4
4. Neela’s clock is broken. The minute hand rotates around the clock correctly, but the hour hand is stuck in the three o’clock position. Suppose Neela first looks at the clock when the hands are aligned and it shows 3:15. She looks at the clock again and sees that the hour and minute hands of the clock form the arms of an angle measuring −105°. How many degrees could the minute hand have rotated to reach its current position?
The answer is –465 degrees
6. If sin θ = one-half , which could not be the value of θ?
The answer is 210 degrees
7. For which value of θ is tan θ equal to sin θ?
The answer is 2pi
8. A gazebo is located in the center of a large, circular lawn with a diameter of 200 feet. Straight paths extend from the gazebo to a sidewalk around the lawn. If two of the paths form a 75° angle, how far would you have to travel around the sidewalk to get from one path to the other? Round your answer to the nearest foot if necessary.
The answer is 131 ft
9. If cos 67° is close to two-fifths, which is closest to the length of modifying above upper N upper O with bar? P-O is 100 cm and angle p is 23 degrees.
The answer is 40 cm
10.
What is the graph of one cycle of a sine curve with the given characteristics? Using the form y = a sin bθ, what is an equation for the sine curve?
amplitude = 4, period = one-fourthpi, and a < 0.
11. A sine function can be used to model light waves. Green light has a wavelength, or period, of about 530 nanometers (nm). Which equation best models green light?
The answer is y=sin pi/265 0
12. Find the period, range, and amplitude of the cosine function.
y = –4 cos 8x
The answer is period= ¼ pi, range= -4<_ y<_4, amplitude=4
13. For a particular angle Θ, the cosine function f(x) = a cos b(Θ) has the following values within one cycle of the function:
The figure shows a list of 5 function values.
f left parenthesis 0 right parenthesis equals 4 semi colon
What is the rule for the cosine function?
Answer is y=4 cos 20
14. What is the value of tan (–Start Fraction 2 pi over 3 End Fraction)?
Answer is pi 3
15. Find the exact value.
tan 45°
Answer is 1
18. What is the value of cos pi over 4?
Answer is
19. Simplify the trigonometric expression.
Start Fraction cosine squared theta over 1 minus sine theta End Fraction
Answer is 1+sin0
20. Use the unit circle to find the inverse function value in degrees.
sin–1Question 3
Answer is 60 degrees
21. Which is the radian measure of an angle whose sine is 0.8? Round your answer to two decimal places.
Answer is 0.93
22. Which is the degree measure of an angle whose tangent is 5.67? Round the answer to the nearest whole number.
Answer is 80 degrees
23. What values for θ (0 ≤ θ ≤ 2π) satisfy the equation?
2 sin θ cos θ + Start Root 3 End Root cos θ = 0
Answer is pi/2, 4pi/3, 3pi/2, 5pi/3
24. For a standard-position angle determined by the point (x,y), what are the values of the trigonometric functions? For this point (5,12), find csc 0 and sec 0.
Answer is csc 0=13/12, sec0=13/5
1 answer