SaiBook.us SAT-2

Home Course Section

Schedule Admission Social

Lesson Example Discussion Quiz: Class Homework

Step-3

Title: Trigonometry equations

Grade: 10-a Lesson: S3-L5

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Solve the equation: \$sin(2x) = 1/2\$ on (0,2π).
2	Step	The given equation is	\$sin(2x) = 1/2\$ on (0,2π)
3	Hint	If \$sin(θ) = 1/2\$, we know θ is in quadrants II and III. While \$θ = sin−1(1/2)\$. Therefore, the possible angles are \$θ = (pi)/6 and (5pi)/6\$.
4	Step	In quadrant II \$2x = (pi)/6\$	\$2x = (pi)/6 + (2pi)\$
5	Step	After simplifying the equation	\$2x = ((pi) + (12pi)) / 6\$ \$x = (13pi)/(12)\$
6	Step	In quadrant IIi \$2x = (5pi)/6\$	\$2x =(5pi)/6 + (2pi)\$
7	Step	After performing simplification	\$2x = ((5pi) + (12pi)) /6\$ \$x = (17pi) / (12)\$
8	Step	So, the solutions for θ are \$(13pi)/12 and (17pi)/12 \$.
9	Choice.A	This choice is incorrect. The provided solutions do not lie within the specified interval	\$(13pi)/12, (12pi)/13\$
10	Choice.B	This solution is accurate because the calculations were done correctly	\$(13pi)/12, (17pi)/12\$
11	Choice.C	This choice is incorrect, as \$(12pi)/17\$ is outside the given interval	\$(13pi)/12, (12pi)/17\$
12	Choice.D	This option is incorrect. The \$(12pi)/13\$ is not a solution within the specified interval, and \$(17pi)/12\$ is correct	\$(12pi)/13, (17pi)/12\$
13	Answer	Option	B
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Solve the equation: \$sin(2x) = 1/2\$ on (0,2π).

Step

The given equation is

\$sin(2x) = 1/2\$ on (0,2π)

Hint

If \$sin(θ) = 1/2\$, we know θ is in quadrants II and III. While \$θ = sin−1(1/2)\$. Therefore, the possible angles are \$θ = (pi)/6 and (5pi)/6\$.

Step

In quadrant II \$2x = (pi)/6\$

\$2x = (pi)/6 + (2pi)\$

Step

After simplifying the equation

\$2x = ((pi) + (12pi)) / 6\$

\$x = (13pi)/(12)\$

Step

In quadrant IIi \$2x = (5pi)/6\$

\$2x =(5pi)/6 + (2pi)\$

Step

After performing simplification

\$2x = ((5pi) + (12pi)) /6\$

\$x = (17pi) / (12)\$

Step

So, the solutions for θ are \$(13pi)/12 and (17pi)/12 \$.

Choice.A

This choice is incorrect. The provided solutions do not lie within the specified interval

\$(13pi)/12, (12pi)/13\$

Choice.B

This solution is accurate because the calculations were done correctly

\$(13pi)/12, (17pi)/12\$

Choice.C

This choice is incorrect, as \$(12pi)/17\$ is outside the given interval

\$(13pi)/12, (12pi)/17\$

Choice.D

This option is incorrect. The \$(12pi)/13\$ is not a solution within the specified interval, and \$(17pi)/12\$ is correct

\$(12pi)/13, (17pi)/12\$

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?