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Worksheet: Inverse Trigonometric Functions

Q1:

A rocket took off from a launchpad and traveled directly upward. When the rocket was 15 miles up, one of the astronauts looked down at the mission control center, which is 2 miles away from the launchpad. What was the angle of depression from her to the mission control center? Round your answer to two decimal places.

Q2:

Find the exact value of t a n t a n βˆ’ 1 ο€Ό 4 πœ‹ 3  , in radians in terms of πœ‹ , which is located in the 1st quadrant.

  • A βˆ’ 4 πœ‹ 3
  • B 2 πœ‹ 3
  • C βˆ’ πœ‹ 3
  • D πœ‹ 3
  • E πœ‹

Q3:

A rocket is launched vertically upward. A woman, standing 4 miles from the launch pad, watches its flight. What is the angle of elevation of the rocket from the woman when its altitude is 11 miles?

Q4:

A ladder is leaning against a vertical wall such that the top is 9 m above the ground and its base is 3 m from the bottom of the wall. Find the measure of the angle between the ladder and the ground. Give your answer to two decimal places.

Q5:

Find the exact value of s i n s i n βˆ’ 1 ο€» πœ‹ 3  in radians.

  • A 4 πœ‹ 3
  • B πœ‹ 6
  • C πœ‹
  • D πœ‹ 3
  • E βˆ’ πœ‹ 3

Q6:

If you drive 0.6 miles along the road and your altitude increases by 150 feet, what is the angle of inclination of the road? Give your answer to two decimal places. Note that 1 mile = 5 2 8 0 feet.

Q7:

A boat is 530 meters away from the base of a 400-meter high cliff. Find the angle of depression of the boat from the top of the cliff giving the answer in radians to three decimal places.

  • A 1.325 rad
  • B 0.647 rad
  • C 0.855 rad
  • D 0.924 rad
  • E 1.569 rad

Q8:

A 90-foot tall building has a shadow that is 2 feet long. What is the angle of elevation of the sun?

Q9:

A woman stands 6 feet from a vertical wall. A footlight on the ground 3 feet from where she is standing is switched on. If the woman is 5 feet tall and her shadow is 15 feet tall, what angle does the light make with the horizontal? Give your answer to two decimal places.

Q10:

Find the exact value of s i n s i n βˆ’ 1 βˆ’ 1 ο€Ό 3 5  + ο€Ό 4 5  in radians.

  • A πœ‹ 4
  • B πœ‹ 3
  • C πœ‹ 6
  • D πœ‹ 2
  • E πœ‹