Big Trig Review
Simplify each expression to a single trig function or number. 1. sec θ sin θ
2. cos θ tan θ 2
2
2
3. tan θ – sec θ 4. 1 – cos θ 5.( 1− cos θ)(1+ cos θ)
6. (sec x −1)(sec x +1)
15.
16.
17. If cot θ= 7 and π < θ < 2π , sketch the angle θ and find the exact value of the other five trig functions. Find the exact value.
18.
19.
20.
21.
22.
23.
24.
25. Through how many radians does the second hand of a clock move in 2 minutes and 40 seconds? 26. A pilot in a plane at an altitude of 22,000 feet observes that the angle of
0
depression to a nearby airport is 26
. How many miles is the airport from the point on the ground directly below the plane?
27. From a point on level ground 145 feet from the base of a tower, the angle
0
of elevation to the top of the tower is 57.3
. How high is the tower? 28. A lighthouse keeper 100 feet above the water sees a boat sailing in a straight line directly toward her. As she watches, the angle of depression to
0
0 the boat changes from 25 to 40 . How far has the boat traveled during this time? [use the Law of Sines] 29. A neighborhood carnival has a Ferris wheel whose radius is 30 feet. You measure the the time it takes for one revolution to be 70 seconds.
a)What is the angular speed in radians per second? b) what is the linear speed in ft/sec?
30. The 25,000 pound Hubble space telescope was launched April 1990 and placed in a 380 mile circular orbit above the earth’s surface. It completes one orbit every 97 minutes, going from a dawn‐to‐dusk cycle nearly 15 times a day. If the radius of the earth is 3964 miles, what is the linear velocity of the space telescope in miles per hour?
30) rθ/t
((4344mi)(2π)/97min)(60min/1hr)
168882.98 mph
31. Solve for θ in both radians and degrees
31) l=rθ
10=9θ
10/9=θ
10rad/9(180°/πrad)
1800°/9π=64°
32. A pizza has a radius of 8.2 inches. A slice cut from
2. cos θ tan θ 2
2
2
3. tan θ – sec θ 4. 1 – cos θ 5.( 1− cos θ)(1+ cos θ)
6. (sec x −1)(sec x +1)
15.
16.
17. If cot θ= 7 and π < θ < 2π , sketch the angle θ and find the exact value of the other five trig functions. Find the exact value.
18.
19.
20.
21.
22.
23.
24.
25. Through how many radians does the second hand of a clock move in 2 minutes and 40 seconds? 26. A pilot in a plane at an altitude of 22,000 feet observes that the angle of
0
depression to a nearby airport is 26
. How many miles is the airport from the point on the ground directly below the plane?
27. From a point on level ground 145 feet from the base of a tower, the angle
0
of elevation to the top of the tower is 57.3
. How high is the tower? 28. A lighthouse keeper 100 feet above the water sees a boat sailing in a straight line directly toward her. As she watches, the angle of depression to
0
0 the boat changes from 25 to 40 . How far has the boat traveled during this time? [use the Law of Sines] 29. A neighborhood carnival has a Ferris wheel whose radius is 30 feet. You measure the the time it takes for one revolution to be 70 seconds.
a)What is the angular speed in radians per second? b) what is the linear speed in ft/sec?
30. The 25,000 pound Hubble space telescope was launched April 1990 and placed in a 380 mile circular orbit above the earth’s surface. It completes one orbit every 97 minutes, going from a dawn‐to‐dusk cycle nearly 15 times a day. If the radius of the earth is 3964 miles, what is the linear velocity of the space telescope in miles per hour?
30) rθ/t
((4344mi)(2π)/97min)(60min/1hr)
168882.98 mph
31. Solve for θ in both radians and degrees
31) l=rθ
10=9θ
10/9=θ
10rad/9(180°/πrad)
1800°/9π=64°
32. A pizza has a radius of 8.2 inches. A slice cut from