A. Incorrect! For a point to lie on the unit circle, the sum of the squares of its coordinates must be equal to 1.

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1 Algebra - Problem Drill 19: Basic Trigonometry - Right Triangle No. 1 of Which of the following points lies on the unit circle? (A) 1, 1 (B) 1, (C) (D) (E), 3, 3, For a point to lie on the unit circle, the sum of the squares of its coordinates must be equal to 1. For a point to lie on the unit circle, the sum of the squares of its coordinates must be equal to 1. C. Correct! The sum of the squares of the coordinates of this point equals 4/4 1. Therefore, this point does lie on the unit circle. For a point to lie on the unit circle, the sum of the squares of its coordinates must be equal to 1. For a point to lie on the unit circle, the sum of the squares of its coordinates must be equal to 1. ( ) ( ) Therefore, the point, of its coordinates is equal to 1. lies on the unit circle because the sum of the squares The correct answer is (C).

2 No. of 10. Calculate the length of the hypotenuse of the right triangle. (A) 3 (B) 7 (C) 7 (D) 7 (E) 9 Use the Pythagorean theorem to find the length of the hypotenuse. Use the Pythagorean theorem to find the length of the hypotenuse. Use the Pythagorean theorem to find the length of the hypotenuse. Use the Pythagorean theorem to find the length of the hypotenuse. E. Correct! You used the Pythagorean theorem to find the length of the hypotenuse. Use the Pythagorean theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the two remaining sides of the right triangle. r a + b r r r r 9 The correct answer is (E).

3 No. 3 of Find cot θ for the indicated point lying on the unit circle. (A) - 3 (B) (C) 3 1 (D) (E) 3 3 A. Correct! You found cot θ by dividing the x-coordinate by the y-coordinate to get - 3. Find cot θ by dividing the x-coordinate by the y-coordinate. Find cot θ by dividing the x-coordinate by the y-coordinate. Find cot θ by dividing the x-coordinate by the y-coordinate. E Incorrect! Find cot θ by dividing the x-coordinate by the y-coordinate. Find cot θ by dividing the x-coordinate by the y-coordinate. cot θ The correct answer is (A).

4 No. 4 of Find the fundamental period of the function shown within the figure. (A) (B) 4 (C) 6 (D) 8 (E) 16 The fundamental period is the length of the smallest interval on which the function repeats itself. The fundamental period is the length of the smallest interval on which the function repeats itself. The fundamental period is the length of the smallest interval on which the function repeats itself. D. Correct! The length of the smallest interval on which this function repeats itself is 8. The fundamental period is the length of the smallest interval on which the function repeats itself. The fundamental period is equal to the length of the smallest interval on which the function repeats itself. The graph of this function starts at x -8 and ends at x 8. The graph does not repeat a y-value until x 0. The length of the interval from -8 to 0 is 8 so; the fundamental period is equal to 8. The correct answer is (D).

5 No. 5 of Which of the following angles does not belong to the domain of sec θ? (A) 0 (B) 45 (C) 180 (D) 70 (E) 330 Sec θ is defined for θ 0. Therefore, 0 belongs to the domain of sec θ. Sec θ is defined for θ 45. Therefore, 45 belongs to the domain of sec θ. C Incorrect! Sec θ is defined for θ 180. Therefore, 180 belongs to the domain of sec θ. D. Correct! Sec θ is undefined for θ 70. Therefore, 70 does not belong to the domain of sec θ. Sec θ is defined for θ 330. Therefore, 330 belongs to the domain of sec θ. An angle will belong to the domain of sec θ if the function is defined for that particular angle. Conversely, an angle will not belong to the domain of sec θ if the function is not defined for that particular angle. The angles for which secant is undefined are equal to odd multiples of π/ and π/ is equal to 90. Therefore, the only angles not belonging to the domain of sec θ are odd multiples of 90. The only degree measurement listed that is equal to an odd multiple of 90 is 70. The correct answer is (D).

6 No. 6 of 10 Instruction: (1) Read the problem statement and answer choices carefully () Work the problems on paper as 6. A calculator does not have a button for csc θ. Which of the following sequences of keystrokes can be used to calculate csc θ? (A) First press cos and then press 1/x. (B) First press sin and then press 1/x. (C) First press tan and then press 1/x. (D) First press 1/x and then press cos. (E) First press 1/x and then press sin. To calculate csc θ, first press the key that corresponds to the reciprocal of csc θ and then press the reciprocal key (1/x). B. Correct! This is correct because sin θ is the reciprocal of csc θ and must be pressed prior to reciprocal key (i.e., 1/x). To calculate csc θ, first press the key that corresponds to the reciprocal of csc θ and then press the reciprocal key (1/x). To calculate csc θ, first press the key that corresponds to the reciprocal of csc θ and then press the reciprocal key (1/x). To calculate csc θ, first press the key that corresponds to the reciprocal of csc θ and then press the reciprocal key (1/x). Csc θ can be calculated by first pressing the key that corresponds to the reciprocal of csc θ followed by pressing the reciprocal key (1/x). Sin θ is the reciprocal of csc θ so, first press sin and then press 1/x. The correct answer is (B).

7 No. 7 of 10 π π 7. What is cos given that sin 0.387? (A) ± (B) ±0.184 (C) ± (D) ±0.939 (E) ± Use the Pythagorean identity Use the Pythagorean identity Use the Pythagorean identity π π sin cos 1 + to find cos 8 π. π π sin cos 1 + to find cos 8 π. π π sin cos 1 + to find cos 8 π. D. Correct! This is the pair of numbers that we obtain by using the Pythagorean identity, π π sin + cos 1. Use the Pythagorean identity π π sin cos 1 + to find cos 8 π. Use the Pythagorean identity π π sin cos 1 + to find cos 8 π. π (0.387) + cos 1 8 π cos 1 8 π cos π cos π cos ± The correct answer is (D).

8 No. 8 of Which of the following sets belongs to both the range of cosine and the range of secant? (A) {-1, 1} (B) {0} (C) all real numbers between -1 and 1 (D) the set of all real numbers (E)(-, -1] and [1, ) A. Correct! -1 and 1 are the only two numbers that belong to both the range of cosine and the range of secant. 0 belongs to the range of cosine but not the range of secant. All real numbers between -1 and 1 belong to the range of cosine but not to the range of secant. Neither the range of cosine nor the range of secant consists of the entire set of real numbers. The intervals (-, -1] and [1, ) belong to the range of secant but not to the range of cosine. The range of cosine consists of all real numbers less than or equal to 1 and greater than or equal to -1. Therefore, both -1 and 1 belong to the domain of cosine. The range of secant consists of all real numbers either greater than or equal to 1 or less than or equal to -1. Therefore, both -1 and 1 belong to the domain of secant. It follows that both -1 and 1 belong the range of cosine and to the range of secant. The correct answer is (A).

9 No. 9 of Calculate the length of the leg opposite the angle with measure 5 of the given right triangle. (A).113 (B).33 (C) (D) (E) 1.34 A. Correct! This is the number obtained by using the formula opposite 5 sin 5. Use the trigonometric function that relates the opposite side and the hypotenuse. Use the trigonometric function that relates the opposite side and the hypotenuse. Use the trigonometric function that relates the opposite side and the hypotenuse. Use the trigonometric function that relates the opposite side and the hypotenuse. Use the formula that will yield the length of the opposite side given the length of the hypotenuse: opposite 5 sin 5 opposite opposite.113 The correct answer is (A).

10 No. 10 of Calculate the length of the side adjacent to the angle with measure given right triangle. π 5 of the (A).167 (B).74 (C) (D) 7.36 (E) Use the trigonometric function that relates the opposite leg to the adjacent leg. B. Correct! This is the number obtained by using the formula adjacent 7 π. tan 5 Use the trigonometric function that relates the opposite leg to the adjacent leg. Use the trigonometric function that relates the opposite leg to the adjacent leg. Use the trigonometric function that relates the opposite leg to the adjacent leg. Use the formula that will yield the length of the adjacent side given the length of the opposite side π adjacent 7 cot 5 Most calculators do not have a key for cotangent (i.e., cot), so use the fact that the reciprocal of cotangent is tangent (i.e., use the fact that cotangent is equal to the reciprocal of tangent). adjacent 7 π tan 5 7 adjacent adjacent.74 The correct answer is (B).