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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Inverse Trigonometric Functions

Grade: 1300-a Lesson: S3-L8

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 right circular cone has a slant height of 10 cm and a base radius of 6 cm. Find the angle at the vertex of the cone using inverse trigonometric functions.	A) 36.87 degrees B) 90 degrees C) 53.13 degrees D) 45 degrees
2	Evaluate \$sin^(-1)(\sqrt3/2) + cos^(-1)(1/2)\$.	A) 1.21 B) 1.6 C) 2.12 D) 2.45
3	If \$tan^(-1)(x) + tan^(−1)(y) = (π/4)\$, what is the value of x + y when xy = 1?	A) 0 B) 1 C) -1 D) \$\sqrt(2)\$
4	Prove that \$1/2\$ ≤ x ≤ 1, then \$ cos^(-1)(x) + cos^(-1)( x/2 + (\sqrt(3) - 3x^2)/2) = pi/3 \$?	A) LHS = RHS B) \$LHS ne RHS\$ C) LHS = 0 D) RHS = infinite
5	solve the following equation: \$2 tan^(-1) (sin x) = tan^(-1) (2 sec x)\$	A) \$x = (pi/2)\$ B) \$x = (pi)\$ C) \$x = (2pi)\$ D) \$x = (pi/3)\$
6	Solve for x in the equation \$ sin^(−1)(2x−1) + cos^(−1)(x) = π/2 \$, where x ∈ [0,1].	A) x = 0 B) x = 1 C) x = 2 D) x = 3
7	Determine the exact value of \$ tan^(−1)(1) + cot^(−1)(3) \$.	A) \$ cot^-1(-2) \$ B) \$ tan^-1(2) \$ C) \$ cot^-1(3) \$ D) \$ tan^-1(1/2) \$
8	If \$ tan^(−1)(a) + tan^(−1)(b) + tan^(−1)(c) = π \$, where a,b,c are positive real numbers, prove that abc=1.	A) Not Proved B) 1 C) Proved D) 0
9	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) 6 meters D) 8 meters
10	Solve for x in the equation \$ sin^(−1)(4x) = π/4 \$.	A) \$(sqrt5)/8 \$ B) \$ (sqrt3)/8 \$ C) \$ (sqrt1)/8 \$ D) \$ (sqrt2)/8 \$

Problem Id

Problem

Options

A right circular cone has a slant height of 10 cm and a base radius of 6 cm. Find the angle at the vertex of the cone using inverse trigonometric functions.

A) 36.87 degrees

B) 90 degrees

C) 53.13 degrees

D) 45 degrees

Evaluate \$sin^(-1)(\sqrt3/2) + cos^(-1)(1/2)\$.

A) 1.21

B) 1.6

C) 2.12

D) 2.45

If \$tan^(-1)(x) + tan^(−1)(y) = (π/4)\$, what is the value of x + y when xy = 1?

A) 0

B) 1

C) -1

D) \$\sqrt(2)\$

Prove that \$1/2\$ ≤ x ≤ 1, then \$ cos^(-1)(x) + cos^(-1)( x/2 + (\sqrt(3) - 3x^2)/2) = pi/3 \$?

A) LHS = RHS

B) \$LHS ne RHS\$

C) LHS = 0

D) RHS = infinite

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

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

B) \$x = (pi)\$

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

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

Solve for x in the equation \$ sin^(−1)(2x−1) + cos^(−1)(x) = π/2 \$, where x ∈ [0,1].

A) x = 0

B) x = 1

C) x = 2

D) x = 3

Determine the exact value of \$ tan^(−1)(1) + cot^(−1)(3) \$.

A) \$ cot^-1(-2) \$

B) \$ tan^-1(2) \$

C) \$ cot^-1(3) \$

D) \$ tan^-1(1/2) \$

If \$ tan^(−1)(a) + tan^(−1)(b) + tan^(−1)(c) = π \$, where a,b,c are positive real numbers, prove that abc=1.

A) Not Proved

B) 1

C) Proved

D) 0

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) 6 meters

D) 8 meters

Solve for x in the equation \$ sin^(−1)(4x) = π/4 \$.

A) \$(sqrt5)/8 \$

B) \$ (sqrt3)/8 \$

C) \$ (sqrt1)/8 \$

D) \$ (sqrt2)/8 \$