SaiBook.us SAT-3

Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Trigonometry

Grade: Best-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: in Class

Problem Id	Problem	Options
1	Solve for x in the equation \$ sin^2(x) + 2^cos(x) = 3 \$, where 0 ≤ x < 2π.	A) \$ x = 1, ((pi)/4), ((3pi)/2) \$ B) \$ x = 0, ((pi)/2), ((3pi)/2) \$ C) \$ x = 1, ((pi)/4), ((3pi)/4) \$ D) \$ x = 0, ((pi)/2), ((3pi)/4) \$
2	A point on the circumference of a circle with a radius of 5 meters subtends an angle of \$ 5π/6 \$ radians at the center. What is the length of the corresponding arc?	A) \$ (21pi)/6 \$ B) \$ (29pi)/6 \$ C) \$ (25pi)/6 \$ D) \$ (23pi)/6 \$
3	From the top of a tower, the angle of depression to a car on the road is 60 degrees. If the tower is 40 meters high, how far is the car from the base of the tower?	A) \$ (40\sqrt3)/3 \$ meters B) \$ (20\sqrt3)/3 \$ meters C) \$ (10\sqrt3)/3 \$ meters D) \$ (30\sqrt3)/3 \$ meters
4	"A ladder is leaning against a wall. If the angle between the ladder and the ground is \$ sin^(−1)(0.8) \$ and the ladder is 10 meters long, how far is the base of the ladder from the wall?	A) 12 meters B) 10 meters C) 8 meters D) 6 meters
5	Solve the equation \$ tan(x) = (2sin(x))/(3 − cos(x)) \$ for 0° ≤ x ≤ 360°.	A) \$ x = 0°,180°,270° \$ B) \$ x = 0°,90°,360° \$ C) \$ x = 0°,180°,360° \$ D) \$ x = 90°,180°,360° \$
6	Prove that \$ (sinx + cosx)/(sinx - cosx) + (sinx - cosx)/(sinx - cosx) = 2/(2 sin^2 x - 1) \$.	A) \$LHS ne RHS\$ B) \$LHS < RHS\$ C) \$LHS > RHS\$ D) LHS = RHS
7	An airplane propeller spins at a rate of 2400 revolutions per minute. Through how many radians does it turn in 3 minutes?	A) 28450π radians B) 14400π radians C) 18110π radians D) 28686π radians
8	An explorer travels 100 miles east, 200 miles north, and 250 miles on a bearing of \$330^\circ\$. Determine the explorer’s final position relative to the starting point using the Law of Sines and the Law of Cosines.	A) (375 miles, \$210^\circ\$) B) (350 miles, \$30^\circ\$) C) (150 miles, \$300^\circ\$) D) (350 miles, \$150^\circ\$)
9	Solve the following equation: \$2 tan^(-1) (sin x) = tan^(-1) (2 sec x)\$	A) \$x = (2pi)\$ B) \$x = (pi)\$ C) \$x = (pi/3)\$ D) \$x = (pi/2)\$
10	A pendulum swings back and forth, completing 20 oscillations every 30 seconds. What is the total angular displacement of the pendulum in radians during this time?	A) \$(\pi/6)\$ radians B) \$(\pi/3)\$ radians C) \$(40\pi)\$ radians D) \$(260\pi)\$ radians

Problem Id

Problem

Options

Solve for x in the equation \$ sin^2(x) + 2^cos(x) = 3 \$, where 0 ≤ x < 2π.

A) \$ x = 1, ((pi)/4), ((3pi)/2) \$

B) \$ x = 0, ((pi)/2), ((3pi)/2) \$

C) \$ x = 1, ((pi)/4), ((3pi)/4) \$

D) \$ x = 0, ((pi)/2), ((3pi)/4) \$

A point on the circumference of a circle with a radius of 5 meters subtends an angle of \$ 5π/6 \$ radians at the center. What is the length of the corresponding arc?

A) \$ (21pi)/6 \$

B) \$ (29pi)/6 \$

C) \$ (25pi)/6 \$

D) \$ (23pi)/6 \$

From the top of a tower, the angle of depression to a car on the road is 60 degrees. If the tower is 40 meters high, how far is the car from the base of the tower?

A) \$ (40\sqrt3)/3 \$ meters

B) \$ (20\sqrt3)/3 \$ meters

C) \$ (10\sqrt3)/3 \$ meters

D) \$ (30\sqrt3)/3 \$ meters

"A ladder is leaning against a wall. If the angle between the ladder and the ground is \$ sin^(−1)(0.8) \$ and the ladder is 10 meters long, how far is the base of the ladder from the wall?

A) 12 meters

B) 10 meters

C) 8 meters

D) 6 meters

Solve the equation \$ tan(x) = (2sin(x))/(3 − cos(x)) \$ for 0° ≤ x ≤ 360°.

A) \$ x = 0°,180°,270° \$

B) \$ x = 0°,90°,360° \$

C) \$ x = 0°,180°,360° \$

D) \$ x = 90°,180°,360° \$

Prove that \$ (sinx + cosx)/(sinx - cosx) + (sinx - cosx)/(sinx - cosx) = 2/(2 sin^2 x - 1) \$.

A) \$LHS ne RHS\$

B) \$LHS < RHS\$

C) \$LHS > RHS\$

D) LHS = RHS

An airplane propeller spins at a rate of 2400 revolutions per minute. Through how many radians does it turn in 3 minutes?

A) 28450π radians

B) 14400π radians

C) 18110π radians

D) 28686π radians

An explorer travels 100 miles east, 200 miles north, and 250 miles on a bearing of \$330^\circ\$. Determine the explorer’s final position relative to the starting point using the Law of Sines and the Law of Cosines.

A) (375 miles, \$210^\circ\$)

B) (350 miles, \$30^\circ\$)

C) (150 miles, \$300^\circ\$)

D) (350 miles, \$150^\circ\$)

Solve the following equation:
\$2 tan^(-1) (sin x) = tan^(-1) (2 sec x)\$

A) \$x = (2pi)\$

B) \$x = (pi)\$

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

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

A pendulum swings back and forth, completing 20 oscillations every 30 seconds. What is the total angular displacement of the pendulum in radians during this time?

A) \$(\pi/6)\$ radians

B) \$(\pi/3)\$ radians

C) \$(40\pi)\$ radians

D) \$(260\pi)\$ radians