Lesson Example Discussion Quiz: Class Homework |
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 |
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 |
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: |
A) Not proved B) 1 C) 0 D) Proved |
6 |
If 3 cot A = 4, check whether |
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: |
A) Not proved B) Infinity C) Proved D) zero |
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