Lesson Example Discussion Quiz: Class Homework |
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 |
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° |
Copyright © 2020-2022 saibook.us Contact: info@saibook.us Version: 1.5 Built: 28-May-2024 09:20AM EST