SaiBook.us SAT-3

Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Trigonometry

Grade: Core-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	Identify the solution to the equation \$3sec^2 (x/2) - 5sec (x/2) - 2 = 0\$ on the interval 0 ≤ x ≤ 2π.	A) \$x = (\pi)/(-3), (5pi)/(-3)\$ B) \$x = (4\pi)/3, (5pi)/3\$ C) \$x = (2\pi)/4, (10pi)/2\$ D) \$x = (2\pi)/3, (10pi)/3\$
2	Identify the solution to the equation \$ 20sin^3(x) + 3 = 12sin^2(x) + 5sin(x) \$ on the interval \$ -π/2 ≤ x ≤ π/2 \$.	A) \$ -pi/6, pi/2, arcsin(3/5) \$ B) \$ -pi/6, pi/6, arcsin(3/5) \$ C) \$ -pi/2, pi/6, arcsin(3/5) \$ D) \$ -pi/2, pi/2, arcsin(1/5) \$
3	What is the supplement of \$(5pi)/6\$ radians in degrees, and what is the complement of 45 degrees in radians?	A) 45, \$ pi/6 \$ B) 45, \$ pi/4 \$ C) 30, \$ pi/4 \$ D) 30, \$ pi/6 \$
4	In a circle with a center O, points A and B are on the circle. If the arc \$\overset{\frown}{AB}\$ measures \$(13π)/15\$ radians, what is the measure of the central angle ∠AOB in degrees?	A) 156 B) 215 C) 181 D) 138
5	If A = \$ \sqrt5\$, B = x, C = 5, and c = 135°. Find the value of x. $2$	A) \$ \sqrt10\$ B) \$\sqrt2\$ C) \$2\sqrt5\$ D) \$5\sqrt2\$
6	In a right triangle, the length of the opposite side to an angle is 6 and the length of the hypotenuse is 12. Find the measure of the angle using the inverse sine function.	A) \$ pi/6 \$ B) \$ pi/8 \$ C) \$ pi/4 \$ D) \$ pi/12 \$
7	Given a triangle where \$A = 40^\circ\$, \$B = 60^\circ\$, and c = 8 units. Find the lengths of the remaining sides and the other angles.	A) \$C = 70^\circ, a = 4.214 "units", "and" b = 7.052 "units"\$ B) \$C = 60^\circ, a = 5.214 "units", "and" b = 6.122 "units"\$ C) \$C = 120^\circ, a = 3.12 "units", "and" b = 7.532 "units"\$ D) \$C = 80^\circ, a = 5.214 "units", "and" b = 7.052 "units"\$
8	Triangle DEF has side DE measuring 6 cm, side EF measuring 9 cm, and the angle between sides DE and EF measures 60 degrees. Find the length of side DF.	A) \$ \sqrt78 \$ B) \$ \sqrt73 \$ C) \$ \sqrt63 \$ D) \$ \sqrt68 \$
9	Evaluate \$ tan^(-1) (1/5) - tan^(-1) (1/70) + tan^(-1) (1/99) \$.	A) \$ pi \$ B) \$- pi/4 \$ C) \$ (3pi)/2\$ D) \$ pi/6 \$
10	If \$ sin^(-1)(x) + sin^(-1)(y) + sin^(-1)(z) = (3pi)/2 \$, then calculate the value of x + y?	A) 5 B) 1 C) 6 D) 2

Problem Id

Problem

Options

Identify the solution to the equation \$3sec^2 (x/2) - 5sec (x/2) - 2 = 0\$ on the interval 0 ≤ x ≤ 2π.

A) \$x = (\pi)/(-3), (5pi)/(-3)\$

B) \$x = (4\pi)/3, (5pi)/3\$

C) \$x = (2\pi)/4, (10pi)/2\$

D) \$x = (2\pi)/3, (10pi)/3\$

Identify the solution to the equation \$ 20sin^3(x) + 3 = 12sin^2(x) + 5sin(x) \$ on the interval \$ -π/2 ≤ x ≤ π/2 \$.

A) \$ -pi/6, pi/2, arcsin(3/5) \$

B) \$ -pi/6, pi/6, arcsin(3/5) \$

C) \$ -pi/2, pi/6, arcsin(3/5) \$

D) \$ -pi/2, pi/2, arcsin(1/5) \$

What is the supplement of \$(5pi)/6\$ radians in degrees, and what is the complement of 45 degrees in radians?

A) 45, \$ pi/6 \$

B) 45, \$ pi/4 \$

C) 30, \$ pi/4 \$

D) 30, \$ pi/6 \$

In a circle with a center O, points A and B are on the circle. If the arc \$\overset{\frown}{AB}\$ measures \$(13π)/15\$ radians, what is the measure of the central angle ∠AOB in degrees?

A) 156

B) 215

C) 181

D) 138

If A = \$ \sqrt5\$, B = x, C = 5, and c = 135°. Find the value of x.

$2$

A) \$ \sqrt10\$

B) \$\sqrt2\$

C) \$2\sqrt5\$

D) \$5\sqrt2\$

In a right triangle, the length of the opposite side to an angle is 6 and the length of the hypotenuse is 12. Find the measure of the angle using the inverse sine function.

A) \$ pi/6 \$

B) \$ pi/8 \$

C) \$ pi/4 \$

D) \$ pi/12 \$

Given a triangle where \$A = 40^\circ\$, \$B = 60^\circ\$, and c = 8 units. Find the lengths of the remaining sides and the other angles.

A) \$C = 70^\circ, a = 4.214 "units", "and" b = 7.052 "units"\$

B) \$C = 60^\circ, a = 5.214 "units", "and" b = 6.122 "units"\$

C) \$C = 120^\circ, a = 3.12 "units", "and" b = 7.532 "units"\$

D) \$C = 80^\circ, a = 5.214 "units", "and" b = 7.052 "units"\$

Triangle DEF has side DE measuring 6 cm, side EF measuring 9 cm, and the angle between sides DE and EF measures 60 degrees. Find the length of side DF.

A) \$ \sqrt78 \$

B) \$ \sqrt73 \$

C) \$ \sqrt63 \$

D) \$ \sqrt68 \$

Evaluate \$ tan^(-1) (1/5) - tan^(-1) (1/70) + tan^(-1) (1/99) \$.

A) \$ pi \$

B) \$- pi/4 \$

C) \$ (3pi)/2\$

D) \$ pi/6 \$

If \$ sin^(-1)(x) + sin^(-1)(y) + sin^(-1)(z) = (3pi)/2 \$, then calculate the value of x + y?

A) 5

B) 1

C) 6

D) 2