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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: Inverse Trigonometric Functions

Grade: 1300-a Lesson: S3-L8

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

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Solve for x: \$2 "tan"^-1("x") = π/3\$.
2	Step	The given equation	\$2 "tan"^-1("x") = π/3\$
3	Step	Divide both sides by 2:	\$(2/2)"tan"^-1("x") = (π/3)/2\$ \$tan^-1("x") = π/6\$
4	Step	Apply the tangent function to both sides to cancel out the inverse tangent:	\$"tan"("tan"^-1("x")) = "tan"(π/6)\$
5	Step	Use the property of inverse and regular tangent functions:	\$("x") = "tan"(π/6)\$
6	Step	Find the value of \$"tan"(π/6)\$:	\$"tan"(π/6) = (\sqrt(3)/3)\$
7	Step	So, the solution for x is \$(\sqrt(3)/3)\$.
8	Choice.A	This is the negative value of the correct solution. In the context of the given equation, it’s not a valid solution	\$-(\sqrt(3)/3)\$
9	Choice.B	This option is the reciprocal of the correct solution. However, the correct solution is \$(\sqrt(3)/3)\$	\$(1/\sqrt(3))\$
10	Choice.C	This is the correct solution obtained by solving the equation \$2 tan^-1(x) = π/3\$	\$(\sqrt(3)/3)\$
11	Choice.D	This is incorrect. It’s the negative of the reciprocal of the correct solution	\$-1/(\sqrt(3))\$
12	Answer	Option	C
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Solve for x: \$2 "tan"^-1("x") = π/3\$.

Step

The given equation

\$2 "tan"^-1("x") = π/3\$

Step

Divide both sides by 2:

\$(2/2)"tan"^-1("x") = (π/3)/2\$

\$tan^-1("x") = π/6\$

Step

Apply the tangent function to both sides to cancel out the inverse tangent:

\$"tan"("tan"^-1("x")) = "tan"(π/6)\$

Step

Use the property of inverse and regular tangent functions:

\$("x") = "tan"(π/6)\$

Step

Find the value of \$"tan"(π/6)\$:

\$"tan"(π/6) = (\sqrt(3)/3)\$

Step

So, the solution for x is \$(\sqrt(3)/3)\$.

Choice.A

This is the negative value of the correct solution. In the context of the given equation, it’s not a valid solution

\$-(\sqrt(3)/3)\$

Choice.B

This option is the reciprocal of the correct solution. However, the correct solution is \$(\sqrt(3)/3)\$

\$(1/\sqrt(3))\$

Choice.C

This is the correct solution obtained by solving the equation \$2 tan^-1(x) = π/3\$

\$(\sqrt(3)/3)\$

Choice.D

This is incorrect. It’s the negative of the reciprocal of the correct solution

\$-1/(\sqrt(3))\$

Answer

Option

Sumup

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