SaiBook.us SAT-3

Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Trigonometry

Grade: Top-SAT3 Lesson: S7-P2

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: at Home

Problem Id	Problem	Options
1	Determine the value of the expression: \$tan^(-1) ((sin(pi/4))/(1 + cos(pi/4)))\$	A) 2.158 B) 2.232 C) 2.274 D) 2.036
2	Given a quadrilateral ABCD with side lengths AB = 8, BC = 15, CD = 12, and angle B = 120 degrees, find the maximum possible area of the quadrilateral.	A) 72 square units B) 60 square units C) 80 square units D) 90 square units
3	Astronomers are calibrating a new telescope to observe celestial objects. Initially, they must point the telescope at an angle of 30 degrees to focus on a star in the southern sky. Later, for a star in the northern sky, the telescope needs to be adjusted to 315 degrees. Convert these angles to radians for the telescope’s control system.	A) \$((2π)/6 , (3π)/4)\$ radians B) \$(π/2 , π/(7/3))\$ radians C) \$(π/6 , (2π)/7)\$ radians D) \$(π/6 , (7π)/4)\$ radians
4	Solve for x in the interval 0 ≤ x < 2π: \$2cos^3 (x) - 3cos^2 (x) + cos(x) = 0\$	A) \$x = (\pi/4), ((5\pi)/4)\$ B) \$x = 0, (\pi)\$ C) \$x = (\pi/2), ((3\pi)/2)\$ D) \$x = (\pi/3), ((2\pi)/3)\$
5	Show that \$ cos^(−1)(x) + cos^(−1)(y) = cos^−1(xy − \sqrt(1 − x^2)(1 - y^2)) \$ for x, y in the appropriate domains.	A) Proved B) 0 C) 1 D) Not Proved
6	An observer on a cliff measures the angles of depression to two ships in the ocean. The angles of depression are 30 degrees and 45 degrees, and the distance between the ships is 10 kilometers. Determine the distance from each ship to the observer using the Law of Sines and Cosines.	A) 5 km and 5 km B) 5 km and \$10\sqrt3\$ km C) \$5\sqrt3\$ km and 10 km D) 5 km and \$5\sqrt3\$ km
7	Identify the general solution to the equation: \$(tanx -1) /( tanx + 1) = - 2\$.	A) \$tan^-1(-1/5) + k(pi)\$ B) \$tan^-1(-1/6) + k(pi)\$ C) \$tan^-1(-1/3) + k(pi)\$ D) \$tan^-1(-1/7) + k(pi)\$
8	At what time between 3 o’clock and 4 o’clock will the minute and hour hands of a clock make an angle closest to 60°? Calculate the time to the nearest second.	A) 4:17 B) 4:48 C) 3:50 D) 3:27
9	An airplane is flying at an altitude of 10,000 meters. From a point on the ground directly below the airplane, the angle of elevation to the airplane is 30°. From another point 5,000 meters away from the first point, the angle of elevation to the airplane is 45°. How high is the airplane?	A) 10,000 meters B) 12,000 meters C) 15,000 meters D) 14,000 meters
10	Solve for x in the equation \$ cos^(−1)(2x^2 − 1) + sin^(−1)(x) = π/2 \$, where x ∈ [−1,1].	A) x = 5 B) x = 1 C) x = 3 D) x = 7

Problem Id

Problem

Options

Determine the value of the expression:
\$tan^(-1) ((sin(pi/4))/(1 + cos(pi/4)))\$

A) 2.158

B) 2.232

C) 2.274

D) 2.036

Given a quadrilateral ABCD with side lengths AB = 8, BC = 15, CD = 12, and angle B = 120 degrees, find the maximum possible area of the quadrilateral.

A) 72 square units

B) 60 square units

C) 80 square units

D) 90 square units

Astronomers are calibrating a new telescope to observe celestial objects. Initially, they must point the telescope at an angle of 30 degrees to focus on a star in the southern sky. Later, for a star in the northern sky, the telescope needs to be adjusted to 315 degrees. Convert these angles to radians for the telescope’s control system.

A) \$((2π)/6 , (3π)/4)\$ radians

B) \$(π/2 , π/(7/3))\$ radians

C) \$(π/6 , (2π)/7)\$ radians

D) \$(π/6 , (7π)/4)\$ radians

Solve for x in the interval 0 ≤ x < 2π:
\$2cos^3 (x) - 3cos^2 (x) + cos(x) = 0\$

A) \$x = (\pi/4), ((5\pi)/4)\$

B) \$x = 0, (\pi)\$

C) \$x = (\pi/2), ((3\pi)/2)\$

D) \$x = (\pi/3), ((2\pi)/3)\$

Show that \$ cos^(−1)(x) + cos^(−1)(y) = cos^−1(xy − \sqrt(1 − x^2)(1 - y^2)) \$ for x, y in the appropriate domains.

A) Proved

B) 0

C) 1

D) Not Proved

An observer on a cliff measures the angles of depression to two ships in the ocean. The angles of depression are 30 degrees and 45 degrees, and the distance between the ships is 10 kilometers. Determine the distance from each ship to the observer using the Law of Sines and Cosines.

A) 5 km and 5 km

B) 5 km and \$10\sqrt3\$ km

C) \$5\sqrt3\$ km and 10 km

D) 5 km and \$5\sqrt3\$ km

Identify the general solution to the equation: \$(tanx -1) /( tanx + 1) = - 2\$.

A) \$tan^-1(-1/5) + k(pi)\$

B) \$tan^-1(-1/6) + k(pi)\$

C) \$tan^-1(-1/3) + k(pi)\$

D) \$tan^-1(-1/7) + k(pi)\$

At what time between 3 o’clock and 4 o’clock will the minute and hour hands of a clock make an angle closest to 60°? Calculate the time to the nearest second.

A) 4:17

B) 4:48

C) 3:50

D) 3:27

An airplane is flying at an altitude of 10,000 meters. From a point on the ground directly below the airplane, the angle of elevation to the airplane is 30°. From another point 5,000 meters away from the first point, the angle of elevation to the airplane is 45°. How high is the airplane?

A) 10,000 meters

B) 12,000 meters

C) 15,000 meters

D) 14,000 meters

Solve for x in the equation \$ cos^(−1)(2x^2 − 1) + sin^(−1)(x) = π/2 \$, where x ∈ [−1,1].

A) x = 5

B) x = 1

C) x = 3

D) x = 7