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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Trigonometry equations

Grade: 1300-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	Prove that \$ ("sinx" + "cosx")/("sinx" - "cosx") + ("sinx" - "cosx")/("sinx" - "cosx") = 2/(2 "sin"^2 "x" - 1) \$.	A) \$"LHS" ne "RHS"\$ B) LHS = RHS C) \$"LHS" < "RHS"\$ D) \$"LHS" > "RHS"\$
2	Prove that of \$ ("sinx")/("secx" + "tanx" - 1) + ("cosx")/("cscx" + "cotx" - 1)\$.	A) Not proved B) 0 C) Proved D) Infinity
3	Solve the equation \$"cos"^3("x") + "sin"^2("x") = 1 \$ for 0° ≤ x ≤ 360°.	A) \$ "x" = 0°, 180°, 360° \$ B) \$ "x" = 0°, 90°, 360° \$ C) \$ "x" = 0°, 270°, 360° \$ D) \$ "x" = 0°, 90°, 270° \$
4	Identify the solutions to the below equation on the interval \$0 le x < 2pi\$. \$ 1/("cotx" - 3) = 1/(2"cotx" - 2) \$.	A) \$ ((3pi)/4), ((7pi)/4) \$ B) \$ ((3pi)/4), ((5pi)/4) \$ C) \$ ((5pi)/4), ((7pi)/4) \$ D) \$ ((3pi)/2), ((7pi)/2) \$
5	Find the values of x satisfying \$"sin"("x") + "cos"("x") = ((\sqrt(2))/2) \$, where 0 ≤ x ≤ 2π.	A) \$ ((pi)/4), ((5pi)/4) \$ B) \$ ((pi)/2), ((5pi)/4) \$ C) \$ ((pi)/4), ((5pi)/2) \$ D) \$ ((pi)/2), ((5pi)/2) \$
6	Find the general solution for x: \$ "cos"(2"x") = 1 - "sin"^2("x") \$	A) \$ (pi)"k" \$ B) \$ ((pi)/2)"k" \$ C) \$ (2pi)"k" \$ D) \$ ((pi)/4)"k" \$
7	Solve the equation \$ "tan"("x") = (2"sin"("x"))/(3 − "cos"("x")) \$ for 0° ≤ x ≤ 360°.	A) \$ "x" = 0°, 180°, 360° \$ B) \$ "x" = 0°, 180°, 270° \$ C) \$ "x" = 0°, 90°, 360° \$ D) \$ "x" = 90°, 180°, 360° \$
8	Solve for x in the equation \$ "sin"^2("x") + 2^"cos"("x") = 3 \$, where 0 ≤ x < 2π.	A) \$ "x" = 0, ((pi)/2), ((3pi)/4) \$ B) \$ "x" = 0, ((pi)/2), ((3pi)/2) \$ C) \$ "x" = 1, ((pi)/4), ((3pi)/2) \$ D) \$ "x" = 1, ((pi)/4), ((3pi)/4) \$
9	Identify all exact solutions to the equation \$ 4("cotx" + 2) = 9 + 3"cotx" \$, 0 ≤ x < 2π.	A) \$ ((pi)/2), ((5pi)/2) \$ B) \$ ((pi)/4), ((5pi)/2) \$ C) \$ ((pi)/4), ((5pi)/4) \$ D) \$ ((pi)/2), ((5pi)/4) \$
10	Solve the equation for x: \$ "sin"(2"x") = "cos"("x") \$.	A) \$ "x" = (((pi)/4) + (2pi)"k"), (((5pi)/6) + (2pi)"k") \$ B) \$ "x" = (((pi)/6) + (2pi)"k"), (((5pi)/4) + (2pi)"k") \$ C) \$ "x" = (((pi)/12) + (2pi)"k"), (((5pi)/12) + (2pi)"k") \$ D) \$ "x" = (((pi)/6) + (2pi)"k"), (((5pi)/6) + (2pi)"k") \$

Problem Id

Problem

Options

Prove that \$ ("sinx" + "cosx")/("sinx" - "cosx") + ("sinx" - "cosx")/("sinx" - "cosx") = 2/(2 "sin"^2 "x" - 1) \$.

A) \$"LHS" ne "RHS"\$

B) LHS = RHS

C) \$"LHS" < "RHS"\$

D) \$"LHS" > "RHS"\$

Prove that of \$ ("sinx")/("secx" + "tanx" - 1) + ("cosx")/("cscx" + "cotx" - 1)\$.

A) Not proved

B) 0

C) Proved

D) Infinity

Solve the equation \$"cos"^3("x") + "sin"^2("x") = 1 \$ for 0° ≤ x ≤ 360°.

A) \$ "x" = 0°, 180°, 360° \$

B) \$ "x" = 0°, 90°, 360° \$

C) \$ "x" = 0°, 270°, 360° \$

D) \$ "x" = 0°, 90°, 270° \$

Identify the solutions to the below equation on the interval \$0 le x < 2pi\$.
\$ 1/("cotx" - 3) = 1/(2"cotx" - 2) \$.

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

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

C) \$ ((5pi)/4), ((7pi)/4) \$

D) \$ ((3pi)/2), ((7pi)/2) \$

Find the values of x satisfying \$"sin"("x") + "cos"("x") = ((\sqrt(2))/2) \$, where 0 ≤ x ≤ 2π.

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

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

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

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

Find the general solution for x:
\$ "cos"(2"x") = 1 - "sin"^2("x") \$

A) \$ (pi)"k" \$

B) \$ ((pi)/2)"k" \$

C) \$ (2pi)"k" \$

D) \$ ((pi)/4)"k" \$

Solve the equation \$ "tan"("x") = (2"sin"("x"))/(3 − "cos"("x")) \$ for 0° ≤ x ≤ 360°.

A) \$ "x" = 0°, 180°, 360° \$

B) \$ "x" = 0°, 180°, 270° \$

C) \$ "x" = 0°, 90°, 360° \$

D) \$ "x" = 90°, 180°, 360° \$

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

A) \$ "x" = 0, ((pi)/2), ((3pi)/4) \$

B) \$ "x" = 0, ((pi)/2), ((3pi)/2) \$

C) \$ "x" = 1, ((pi)/4), ((3pi)/2) \$

D) \$ "x" = 1, ((pi)/4), ((3pi)/4) \$

Identify all exact solutions to the equation
\$ 4("cotx" + 2) = 9 + 3"cotx" \$, 0 ≤ x < 2π.

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

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

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

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

Solve the equation for x:
\$ "sin"(2"x") = "cos"("x") \$.

A) \$ "x" = (((pi)/4) + (2pi)"k"), (((5pi)/6) + (2pi)"k") \$

B) \$ "x" = (((pi)/6) + (2pi)"k"), (((5pi)/4) + (2pi)"k") \$

C) \$ "x" = (((pi)/12) + (2pi)"k"), (((5pi)/12) + (2pi)"k") \$

D) \$ "x" = (((pi)/6) + (2pi)"k"), (((5pi)/6) + (2pi)"k") \$