Inverse Trigonometric Worksheets Grade 11

1. arcsin(1/2) + arccos(1/2) = ?
2. sin(2arctan(4/3)) = ?
3. A marine biologist is studying a coral reef formation. From her research boat, she measures that the reef drops vertically 18 meters below the water surface. Using sonar, she determines that the horizontal distance from her boat to the point directly above the base of the reef is 24 meters. What angle of depression, in degrees, should she calculate for her research notes? Express your answer to the nearest tenth of a degree.

…and 3 more problems

1. 2arctan(1) + arcsin(1/2) = ?
2. sin⁻¹(11/61) + sin⁻¹(60/61) = ?
3. sin(2arctan(1/3)) = ?

…and 5 more problems

1. Tane is a forest ranger monitoring a wildfire from a lookout tower. He spots a smoke plume at an angle of depression of 17° from the tower. The tower is 45 meters tall. Using inverse trigonometric functions, what is the horizontal distance, in meters, from the base of the tower to the smoke plume? Round your answer to the nearest whole meter.
2. Emma is a civil engineer designing a suspension bridge. The main cable of the bridge follows a parabolic curve and is anchored at two towers that are 200 meters apart. At the lowest point of the cable (the vertex), the cable is 20 meters above the deck of the bridge. The cable is attached to each tower at a height of 60 meters above the deck. Emma needs to calculate the angle θ that the cable makes with the horizontal at the point where it attaches to a tower. The relationship is given by tan(θ) = (vertical rise from vertex to tower) / (half the horizontal span). Using an inverse trigonometric function, what is θ in degrees? Round your answer to one decimal place.
3. Hana is a marine biologist tracking a pod of dolphins. She observes a dolphin diving from the surface straight down to a depth of 24 meters. From the point directly above the dolphin on the surface, she measures the horizontal distance to a coral formation on the seafloor to be 32 meters. If the dolphin swims in a straight line from its current depth to the coral formation, what angle, in degrees, does its path make with the horizontal seafloor? Use an inverse trigonometric function and round your answer to the nearest tenth of a degree.

…and 2 more problems