D. Correct! 2 does not belong to the domain of arcsin x.
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1 CLEP Precalculus - Problem Drill 10: Inverse Trigonometry No. 1 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems 1. Which of the following numbers is not in the domain of arcsin x? (A) 0 (B) 1 (C) 1 (D) (E) is in the domain of arcsin x. is in the domain of arcsin x. 1 1 is in the domain of arcsin x. D. Correct! does not belong to the domain of arcsin x. 3 is in the domain of arcsin x. 4 The domain of arcsin x consists of all numbers that are greater than or equal to -1 and less than or equal to 1 (including -1 and 1). Therefore, any number greater than 1 or less than -1 does not belong to the domain of arcsin x. The number is greater than 1. The correct answer is (D).
2 No. of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems. Which of the followings does not belong to the range of arcos x? (A) π (B) 0 (C) 1 (D) π (E) 1 A. Correct! Numbers belonging to the range of arccos x are positive. Therefore, does not belong to the range of arccos x. π Any number between 0 and π (including 0 and π) belongs to the range of arccos x. Therefore, 0 belongs to the range of arccos x. Any number between 0 and π (including 0 and π) belongs to the range of arccos x. Therefore, 1 belongs to the range of arccos x. Any number between 0 and π (including 0 and π) belongs to the range of π arccos x. Therefore, belongs to the range of arccos x. Any number between 0 and π (including 0 and π) belongs to the range of arcos x. Therefore, 1 belongs to the range of arcos x. The range of arccos x consists of all numbers that are simultaneously greater than or equal to 0 less than or equal to π. Therefore, negative numbers do not belong to the range of arccos x. The number is negative. π The correct answer is (A).
3 No. 3 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems 3. Which of the following relations is false? (A) cos(arccos 0.5) = 0.5 (B) arctan(tan ) = (C) tan(arctan ) = (D) arcsin(sin 1) = 1 (E) sin(arcsin 1) = belongs to the domain of arccos x. Therefore, cos(arccos 0.5) = 0.5 is true. B. Correct! does not belong to the range of arctan x. Therefore, arctan(tan ). belongs to the domain of arctan x. Therefore, tan(arctan ) = is true. 1 belongs to the range of arcsin x. Therefore, arcsin(sin 1) = 1 is true. 1 belongs to the domain of arcsin x. Therefore, sin(arcsin 1) = 1 is true. arctan(tan x) = x will only be true if x belongs to the range of arctan. does not belong to the range of arctan x. It follows that arctan(tan ) = is false. The correct answer is (B).
4 No. 4 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems 4. Evaluate sin arcsin. (A) 0 (B) 1 (C) (D) (E) cannot be evaluated Recall the relationship between inverse trigonometric functions and try again. Recall the relationship between inverse trigonometric functions and try again. C. Correct! Since is in the domain of arcsin, the composition of the inverse functions results in the given value. Recall the relationship between inverse trigonometric functions and try again. Recall the relationship between inverse trigonometric functions and try again. is a number within the domain of arcsin. Therefore, sin arcsin = The correct answer is (C)..
5 No. 5 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems 5. Find the length of the adjacent side of the right triangle shown within the figure π/ adj (A) 6.8 (B) 7. (C) 8. (D) 9.9 (E) 14.5 adjacent = hypotenuse cos θ to find the side length. adjacent = hypotenuse cos θ to find the side length. adjacent = hypotenuse cos θ to find the side length. D. Correct! You used the formula adjacent = hypotenuse cos θ to find the side length. adjacent = hypotenuse cos θ to find the side length. Use the following formula to find the length of the adjacent side of the right triangle. adjacent = hypotenuse cos θ adjacent = 1 cos 0.6 adjacent adjacent 9.9 The correct answer is (D).
6 No. 6 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems 6. Find the length of the hypotenuse of the right triangle shown within the figure. hyp 5 1 π/ (A).7 (B) 4. (C) 5.9 (D) 7.8 (E) 9.3 C. Correct! You used the formula hypotenuse = hypotenuse = hypotenuse 5 sin hypotenuse 5.9 The correct answer is (C).
7 No. 7 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems 7. Find the value of the acute angle θ shown in the figure. θ π/ 1.5 (A)0.64 radians (B)0.7 radians (C)0.85 radians (D)0.93 radians (E)undefined θ arctan to find the angle measure. = = arctan θ = arctan to find the angle measure. D. Correct! = arctan You used the formula = arctan = arctan θ = arctan θ = arctan 1.5 θ arctan1.33 θ 0.93 radians The correct answer is (D).
8 No. 8 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems 8. Find the value of the acute angle θ shown in the figure. 8 θ π/ 7 (A) 0.51 radians (B) 0.7 radians (C) 0.85 radians (D) 1.07 radians (E) undefined A. Correct! You used the formula adjacent adjacent adjacent adjacent adjacent adjacent adjacent θ 7 θ = arccos 8 θ = arccos θ 0.51 radians The correct answer is (A).
9 No. 9 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems 9. A person walks due east for 3 miles. The person then walks 4 miles due south. Find the distance and bearing of the final position of the person relative to their initial position. (A) 1 mile, S37 W (B) 1 mile, S53 E (C) 5 miles, N53 W (D) 5 miles, S37 E (E) 7 miles, N37 E Use the Pythagorean theorem and navigation bearings to find the answer. Use the Pythagorean theorem and navigation bearings to find the answer. Use the Pythagorean theorem and navigation bearings to find the answer. D. Correct! Use the Pythagorean theorem and navigation bearings to find the answer of 5 miles, S37 E. Use the Pythagorean theorem and navigation bearings to find the answer. N W 3 E 4 θ 4 S 3 The distance of the person's final position from their initial position is: distance = (3 + 4 ) distance = (9 + 16) distance = 5 distance = 5 The angle θ Is given by: θ = arctan(/adjacent) θ = arctan(3/4) θ = arctan(0.75) θ 37 The final position of the person is south and east of their original position. Therefore, the bearing is S37 E. Thus, the final answer is choice D.
10 No. 10 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems 10. Find angle θ in the figure. 7 θ π/ adjacent = 3 (A) 0.4 radians (B) 1.1 radians (C) 0.9 radians (D).3 radians (E) 4 radians Use the inverse trigonometric function that relates the adjacent side to the hypotenuse. B. Correct! You used arcos to find θ 1.1 radians. Use the inverse trigonometric function that relates the adjacent side to the hypotenuse. Use the inverse trigonometric function that relates the adjacent side to the hypotenuse. Use the inverse trigonometric function that relates the adjacent side to the hypotenuse. cos θ = adjacent hypotenuse adjacent ( θ) arccos cos adjacent θ 3 θ 7 θ 1.1 radians The correct answer is (B).
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