SaiBook.us SAT-3

Lesson Example Discussion Quiz: Class Homework

Quiz At Home

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: at Home

Problem Id	Problem	Options
1	A town planning board wishes to place sod on their village commons that is in the shape of a triangle whose sides have lengths of 120 ft, 165 ft and 200 ft. If the sod costs 0.35 per square foot, determine the cost, to the nearest dollar for covering the common in sod.	A) $3,426 B) $3,624 C) $3,462 D) $3,264
2	Prove \$ tan{ pi/4 + 1/2 cos^(-1) (a/b)} + tan{ pi/4 - 1/2 cos^(-1) (a/b)} = (2b)/a\$.	A) LHS = RHS B) \$LHS ne RHS\$ C) LHS > RHS D) LHS < RHS
3	Identify the general solution to the equation \$ (3 sin^2 x + 2 sinx - 5)/(sin^2 x + sinx - 2) = 0\$.	A) 1 B) Solutions C) 0 D) No solutions
4	A wind farm operator needs to adjust the angles of the blades on a wind turbine for optimal performance based on wind direction. The blades initially face the wind at an angle of 135 degrees. Due to a shift in wind direction, the blades need to be adjusted to 315 degrees. The control software requires these angles to be input in radians.	A) \$(4pi)/3, (4pi)/7\$ B) \$(3pi)/4, (7pi)/4\$ C) \$(3pi)/4, (5pi)/4\$ D) \$(5pi)/4, (7pi)/4\$
5	In triangle PQR, if side p measures 20 units, side q measures 15 units, and angle R measures 60 degrees, find the length of side r.	A) 18.0 units B) 15.8 units C) 16.5 units D) 17.0 units
6	Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation \$cos^-1(x) - 2sin^-1(x) = cos^-1(2x)\$ is equal to:	A) 2 B) 0 C) 3 D) 4
7	Solve the equation exactly: \$2sin^2(θ) - 5sinθ + 3 = 0\$, 0 ≤ θ ≤ 2π.	A) \$4pi\$ B) \$2pi\$ C) \$pi/2\$ D) \$pi/4\$
8	A golfer misses a 12-foot putt by putting 3ºoff course. The hole now lies at a 129º angle between the ball and its spot before the putt. What distance does the golfer need to putt in order to make the shot?	A) 0.58 ft B) 0.65 ft C) 0.56 ft D) 0.85 ft
9	A regular hexagon is inscribed in a circle. What is the measure of the central angle subtended by one side of the hexagon, in degrees and radians?	A) \$pi/3\$ B) \$pi/5\$ C) \$3pi\$ D) \$5pi\$
10	If \$sin^-1(x - (x^2/2) + (x^4/4) - . . . . . .) + cos^-1( x^2 - (x^4/2) + (x^6/4) + . . . . .) = (pi)/2\$ for \$0 < \|x\| < \sqrt2\$, then x equals?	A) - 1 B) 1 C) \$- 1/2\$ D) \$1/2\$

Problem Id

Problem

Options

A town planning board wishes to place sod on their village commons that is in the shape of a triangle whose sides have lengths of 120 ft, 165 ft and 200 ft. If the sod costs 0.35 per square foot, determine the cost, to the nearest dollar for covering the common in sod.

A) $3,426

B) $3,624

C) $3,462

D) $3,264

Prove \$ tan{ pi/4 + 1/2 cos^(-1) (a/b)} + tan{ pi/4 - 1/2 cos^(-1) (a/b)} = (2b)/a\$.

A) LHS = RHS

B) \$LHS ne RHS\$

C) LHS > RHS

D) LHS < RHS

Identify the general solution to the equation \$ (3 sin^2 x + 2 sinx - 5)/(sin^2 x + sinx - 2) = 0\$.

A) 1

B) Solutions

C) 0

D) No solutions

A wind farm operator needs to adjust the angles of the blades on a wind turbine for optimal performance based on wind direction. The blades initially face the wind at an angle of 135 degrees. Due to a shift in wind direction, the blades need to be adjusted to 315 degrees. The control software requires these angles to be input in radians.

A) \$(4pi)/3, (4pi)/7\$

B) \$(3pi)/4, (7pi)/4\$

C) \$(3pi)/4, (5pi)/4\$

D) \$(5pi)/4, (7pi)/4\$

In triangle PQR, if side p measures 20 units, side q measures 15 units, and angle R measures 60 degrees, find the length of side r.

A) 18.0 units

B) 15.8 units

C) 16.5 units

D) 17.0 units

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation \$cos^-1(x) - 2sin^-1(x) = cos^-1(2x)\$ is equal to:

A) 2

B) 0

C) 3

D) 4

Solve the equation exactly: \$2sin^2(θ) - 5sinθ + 3 = 0\$, 0 ≤ θ ≤ 2π.

A) \$4pi\$

B) \$2pi\$

C) \$pi/2\$

D) \$pi/4\$

A golfer misses a 12-foot putt by putting 3ºoff course. The hole now lies at a 129º angle between the ball and its spot before the putt. What distance does the golfer need to putt in order to make the shot?

A) 0.58 ft

B) 0.65 ft

C) 0.56 ft

D) 0.85 ft

A regular hexagon is inscribed in a circle. What is the measure of the central angle subtended by one side of the hexagon, in degrees and radians?

A) \$pi/3\$

B) \$pi/5\$

C) \$3pi\$

D) \$5pi\$

If \$sin^-1(x - (x^2/2) + (x^4/4) - . . . . . .) + cos^-1( x^2 - (x^4/2) + (x^6/4) + . . . . .) = (pi)/2\$ for \$0 < |x| < \sqrt2\$, then x equals?

A) - 1

B) 1

C) \$- 1/2\$

D) \$1/2\$