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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Trigonometry Identities (quotient , co-function)

Grade: 1300-a Lesson: S3-L4

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	Given that \$ cot(pi/2 - x) = tan(x)\$, use this identity to simplify \$cot(pi/2 - 2x)\$.	A) tan(x) B) cot(2x) C) tan(2x) D) cot(x)
2	If tanA + cotA = 2, find sin2A.	A) 4 B) 2 C) \$ 1/2\$ D) 1
3	Prove \$ sin(x + y) sin(x - y) = sin^2 (x) - sin^2 (y)\$.	A) Zero B) Proved C) Not Proved D) Infinity
4	Given that \$sinx = 3/5\$ and x is in the first quadrant, find \$tan(90^\circ - x)\$.	A) \$ 4/3\$ B) \$ 3/5\$ C) \$ 4/5\$ D) \$ 3/4\$
5	Simplify \$ cos(x) csc(pi/2 - x) + sin(x) sec(pi/2 - x)\$.	A) 2 B) 0 C) 4 D) \$ 1/2\$
6	Simplify \$ tan(pi/2 - θ)/cot(pi/2 - θ) \$.	A) \$- tan^2(θ)\$ B) \$cot^2 (θ)\$ C) \$tan^2(θ)\$ D) \$- cot^2(θ)\$
7	A kite is flying in the sky. The length of the string (hypotenuse) is 100 meters, and the kite makes an angle of 30 degrees with the ground. Determine the height of the kite above the ground using the quotient identities.	A) 20 m B) 50 m C) 40 m D) 30 m
8	Prove that \$ tanx + cotx = 2/(sin2x)\$.	A) Not proved B) Zero C) Proved D) 1
9	If \$cos⁡(θ) = 5/13\$ and θ is in the fourth quadrant, find tan⁡(θ).	A) \$- (12)/13\$ B) \$5/(12)\$ C) \$- (12)/5\$ D) \$(13)/12\$
10	Solve for x if \$tan(2x) = cot(x)\$ and x is in the first quadrant.	A) 0° B) 90° C) 180° D) 30°

Problem Id

Problem

Options

Given that \$ cot(pi/2 - x) = tan(x)\$, use this identity to simplify \$cot(pi/2 - 2x)\$.

A) tan(x)

B) cot(2x)

C) tan(2x)

D) cot(x)

If tanA + cotA = 2, find sin2A.

A) 4

B) 2

C) \$ 1/2\$

D) 1

Prove \$ sin(x + y) sin(x - y) = sin^2 (x) - sin^2 (y)\$.

A) Zero

B) Proved

C) Not Proved

D) Infinity

Given that \$sinx = 3/5\$ and x is in the first quadrant, find \$tan(90^\circ - x)\$.

A) \$ 4/3\$

B) \$ 3/5\$

C) \$ 4/5\$

D) \$ 3/4\$

Simplify \$ cos(x) csc(pi/2 - x) + sin(x) sec(pi/2 - x)\$.

A) 2

B) 0

C) 4

D) \$ 1/2\$

Simplify \$ tan(pi/2 - θ)/cot(pi/2 - θ) \$.

A) \$- tan^2(θ)\$

B) \$cot^2 (θ)\$

C) \$tan^2(θ)\$

D) \$- cot^2(θ)\$

A kite is flying in the sky. The length of the string (hypotenuse) is 100 meters, and the kite makes an angle of 30 degrees with the ground. Determine the height of the kite above the ground using the quotient identities.

A) 20 m

B) 50 m

C) 40 m

D) 30 m

Prove that \$ tanx + cotx = 2/(sin2x)\$.

A) Not proved

B) Zero

C) Proved

D) 1

If \$cos⁡(θ) = 5/13\$ and θ is in the fourth quadrant, find tan⁡(θ).

A) \$- (12)/13\$

B) \$5/(12)\$

C) \$- (12)/5\$

D) \$(13)/12\$

Solve for x if \$tan(2x) = cot(x)\$ and x is in the first quadrant.

A) 0°

B) 90°

C) 180°

D) 30°