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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Inverse Trigonometric Functions

Grade: 1400-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	Compute the value of the expression: \$tan^(-1) ((1 + sin(pi/6))/(1 - cos(pi/6)))\$	A) s0.2031 B) 1.5201 C) -0.2031 D) -1.5201
2	Simplify the expression: \$cos(sin^(-1)(2/3)) + sin(cos^(-1)(-1/2))\$	A) 0.589 B) 0.656 C) 0.751 D) 0.862
3	If \$y = sin^(−1)((3x − 4)/5)\$, then what is the range of y?	A) \$0, pi\$ B) \$-pi/2, pi/2\$ C) \$-pi, pi\$ D) \$-pi/4, pi/4\$
4	Determine the value of the expression: \$tan^(-1) ((sin(pi/4))/(1 + cos(pi/4)))\$	A) 2.274 B) 2.232 C) 2.158 D) 2.036
5	If \$cos^(-1)(x) + cos^(-1)(y) = (pi/3)\$, find the value of \$sin^(-1)(x) + sin^(-1)(y)\$.	A) \$pi/2\$ B) \$pi/3\$ C) \$pi/4\$ D) \$pi/6\$
6	Prove that \$ sin^(−1)(x) + tan^(-1)(\sqrt(1 - x^2)/x) = π/2 \$ for x > 0.	A) 1 B) Proved C) 0 D) Not Proved
7	If \$ tan^(−1)(x) = tan^(−1)(y) + tan^(−1)(z) \$, where x,y,z are real numbers, find a relation between x,y,z.	A) \$ x = ((y - z)/(1 - yz)) \$ B) \$ x = ((y + z)/(1 - yz)) \$ C) \$ x = ((y + z)/(1 + yz)) \$ D) \$ x = ((y - z)/(1 + yz)) \$
8	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 = 3 C) x = 1 D) x = 7
9	A car is driving up a hill with an incline of \$ cos^(−1)(0.8) \$. If the car’s speedometer reads 60 km/h, what is its speed along the horizontal component of the hill?	A) \$ 64 ((km)/h) \$ B) \$ 38 ((km)/h) \$ C) \$ 48 ((km)/h) \$ D) \$ 58 ((km)/h)\$
10	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) Not Proved B) 0 C) 1 D) Proved

Problem Id

Problem

Options

Compute the value of the expression:
\$tan^(-1) ((1 + sin(pi/6))/(1 - cos(pi/6)))\$

A) s0.2031

B) 1.5201

C) -0.2031

D) -1.5201

Simplify the expression:
\$cos(sin^(-1)(2/3)) + sin(cos^(-1)(-1/2))\$

A) 0.589

B) 0.656

C) 0.751

D) 0.862

If \$y = sin^(−1)((3x − 4)/5)\$, then what is the range of y?

A) \$0, pi\$

B) \$-pi/2, pi/2\$

C) \$-pi, pi\$

D) \$-pi/4, pi/4\$

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

A) 2.274

B) 2.232

C) 2.158

D) 2.036

If \$cos^(-1)(x) + cos^(-1)(y) = (pi/3)\$, find the value of \$sin^(-1)(x) + sin^(-1)(y)\$.

A) \$pi/2\$

B) \$pi/3\$

C) \$pi/4\$

D) \$pi/6\$

Prove that \$ sin^(−1)(x) + tan^(-1)(\sqrt(1 - x^2)/x) = π/2 \$ for x > 0.

A) 1

B) Proved

C) 0

D) Not Proved

If \$ tan^(−1)(x) = tan^(−1)(y) + tan^(−1)(z) \$, where x,y,z are real numbers, find a relation between x,y,z.

A) \$ x = ((y - z)/(1 - yz)) \$

B) \$ x = ((y + z)/(1 - yz)) \$

C) \$ x = ((y + z)/(1 + yz)) \$

D) \$ x = ((y - z)/(1 + yz)) \$

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 = 3

C) x = 1

D) x = 7

A car is driving up a hill with an incline of \$ cos^(−1)(0.8) \$. If the car’s speedometer reads 60 km/h, what is its speed along the horizontal component of the hill?

A) \$ 64 ((km)/h) \$

B) \$ 38 ((km)/h) \$

C) \$ 48 ((km)/h) \$

D) \$ 58 ((km)/h)\$

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) Not Proved

B) 0

C) 1

D) Proved