Quiz In Class

Title: Trigonometry Identities ( Pythagorean, reciporcal)

Grade: 1400-a Lesson: S3-L3

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: in Class

Problem Id Problem Options

1

If \$"sin"(α)= 12/13 \$and \$"tan"(β) = − 3/4\$, where α and β are acute angles, find sin(α + β).

A) \$ 63/65 \$

B) \$ 61/65 \$

C) \$ 53/56 \$

D) \$ 36/65 \$

2

Use reciprocal identities to simplify
\$ ("csc"^2 ("x") - "cot"^2 ("x"))/("csc"^2 ("x") + "cot"^2 ("x")) \$.

A) \$ ("sin"^2 ("x") )/(- 1 + "cos"^2 ("x") ) \$

B) \$ ("sin"^2 ("x"))/(1 + "cos"^2 ("x") ) \$

C) \$ (2"sin"^2 ("x") )/(1 + "cos"^2 ("x") ) \$

D) \$ ("sin"^2 ("x") )/(2 + 2 "cos"^2 ("x") ) \$

3

Simplify the expression by using reciprocal identity
\$ (1/2) "cot" "x" + (1/2) "tan" "x" \$.

A) sec 2x

B) sin 2x

C) csc 2x

D) cos 2x

4

Verify that the Pythagorean identity relating secant and tangent is true for \$\theta = pi/6 \$.

A) \$ "sec"^2 (pi/6) = \sqrt3/2 \$ and \$ 1 + "tan"^2 (pi/6) = 1/2 \$

B) \$ "sec"^2 (pi/6) = 2/\sqrt3 \$ and \$ 1 + "tan"^2 (pi/6) = 1/\sqrt3 \$

C) \$ "sec"^2 (pi/6) = 3/4 \$ and \$ 1 + "tan"^2 (pi/6) = 3/4 \$

D) \$ "sec"^2 (pi/6) = 4/3 \$ and \$ 1 + "tan"^2 (pi/6) = 4/3 \$

5

Verify the identity:
\$ ("sec" "x" - "tan" "x")/ ("sec" "x") = ("cos"^2 ("x")) / ( 1 + "sin" "x") \$.

A) Not proved

B) 1

C) 0

D) Proved

6

If 3 cot A = 4, check whether
\$(1 – "tan"^2("A"))/(1 + "tan"^2("A"))\$ = \$"cos"^2 ("A") – "sin"^2 ("A")\$.

A) Not proved

B) 0

C) Proved

D) 1

7

Which of the following trigonometric identity is true?

A) \$2"cosx" = ("sinx")/(1 + "cosx") + (1 + "cosx")/("sinx")\$

B) \$2/("sinx") = ("sinx")/(1 + "cosx") + (1 + "cosx")/("sinx")\$

C) \$2"sinx" = ("sinx")/(1 + "cosx") + (1 + "cosx")/("sinx")\$

D) \$2/("cosx") = ("sinx")/(1 + "cosx") + (1 + "cosx")/("sinx")\$

8

Solve \$4/("sec"2(θ)) + 3"cos"(θ) = 2 "cot"(θ) "tan"(θ)\$ for all solutions with 0 ≤ θ < 2π.

A) 5.152

B) 5.125

C) 5.512

D) 5.251

9

Write \$(1 + "cot"^2(θ)) /(1 - "csc"^2(θ))\$ in terms of sinθ and cosθ, and then simplify the expression so that no quotients appear.

A) \$"csc"^2(θ)\$

B) \$- "sec"^2(θ)\$

C) \$- "csc"^2(θ)\$

D) \$"sec"^2(θ)\$

10

Prove the identity:
\$("tanx"/("secx")) . "sin"(- "x") = - "cos"^2("x")\$.

A) Not proved

B) Infinity

C) Proved

D) zero


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