Quiz At Home

Title: Trigonometry equations

Grade: 10-a Lesson: S3-L5

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 \$ 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) \$

2

Solve for x in the equation \$sin(x)= 1/2 \$,​ where 0 ≤ x ≤ 2π.

A) \$ pi/2, (5pi)/2 \$

B) \$ pi/4, (5pi)/4 \$

C) \$ pi/6, (5pi)/6 \$

D) \$ pi/2, (5pi)/6 \$

3

Find the solution of the trigonometric equation
2(tanx + 3) = 5 + tanx.

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

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

C) \$ pi/4, (7pi)/4 \$

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

4

Solve for x in the equation \$2cos^2(x) − 3cos(x) + 1 = 0\$, where 0 ≤ x ≤ 2π.

A) \$ 0, 2pi, (pi)/3, (5pi)/3 \$

B) \$ 0, 3pi, (pi)/2, (5pi)/3 \$

C) \$ 0, 2pi, (pi)/3, (5pi)/2 \$

D) \$ 1, 2pi, (2pi)/3, (4pi)/3 \$

5

Determine all solutions for θ in the equation \$cos(2θ ) = -1/2\$, where 0° ≤ θ ≤ 360°.

A) 60°, 120°, 240°, 300°

B) 60°, 150°, 240°, 300°

C) 60°, 120°, 270°, 300°

D) 60°, 120°, 240°, 320°

6

Identify the solution to the equation \$5tan \theta = -1-3tan^2\theta\$ on the interval \$-π/2 ≤ 0 ≤ π/2\$.

A) \$\theta = arctan((-5-\sqrt13)/6), arctan((-5+\sqrt13)/6)\$

B) \$\theta = arctan((5+\sqrt3)/2), arctan((5-\sqrt3)/2)\$

C) \$\theta = arctan((-5-\sqrt6)/13), arctan((-5+\sqrt6)/13)\$

D) \$\theta = arctan((5-\sqrt13)/6), arctan((5+\sqrt13)/6)\$

7

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

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

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

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

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

8

Identify the general solution to the equation \$csc^2 x - 4csc x + 4 = 0\$.

A) \$x = \pi/5 + 3\pin\$ and \$x = (5\pi) /5 + 3\pi n\$

B) \$x = \pi/6 + \pin\$ and \$x = (5\pi)/6 + 2\pi n\$

C) \$x = \pi/6 - 2\pin\$ and \$x = (5\pi)/6 + 2n\$

D) \$x = \pi/6 - 2\pin\$ and \$x = -(5\pi)/6 + 2\pin\$

9

Identify the solution to the equation \$4cos^2 x - 1 = 0\$ on the interval 0 ≤ x ≤ 2π.

A) \$ \pi/2, (2\pi)/2, (4\pi)/2, (5\pi)/2 \$

B) \$ -\pi/3, (-2\pi)/3, (-4\pi)/3, (-5\pi)/3 \$

C) \$ \pi/3, (2\pi)/3, (4\pi)/3, (5\pi)/3 \$

D) \$ -\pi/2, (-2\pi)/2, (-4\pi)/2, (-5\pi)/2 \$

10

Find all solutions to the equation sin(2x) + cos(x) = 0 for 0 ≤ x ≤ 360.

A) x = 45° or x = 225°

B) x = 60° or x = 240°

C) x = 90° or x = 270°

D) x = 30° or x = 210°


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