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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

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: at Home

Problem Id	Problem	Options
1	Find the value of acute angle x, if tan(x) = cot 10°.	A) 40° B) 70° C) 80° D) 60°
2	Determine the value of cosec 150° using cofunction identities.	A) 1 B) 0 C) undefined D) 2
3	If \$ cosθ = 1/4 \$ and \$ cotθ = 2/\sqrt3 \$, what is the value of sinθ ?	A) \$ \sqrt3/4 \$ B) \$ \sqrt3/8 \$ C) \$ \sqrt3/2 \$ D) \$ \sqrt3/18 \$
4	If cscθ = 0.87 , find \$ sec(θ − pi/2) \$ .	A) 0.87 B) 0.13 C) 0.23 D) 0.77
5	A wheelchair ramp has an angle of elevation of 45 degrees. If the length of the ramp is 12 meters, find the vertical height gain for someone using the ramp.	A) 12 meters B) 13 meters C) 24 meters D) 15 meters
6	Simplify the expression \$ (1 - cos(2x))/(sin(2x)) \$.	A) sec(2x) B) tan(x) C) \$sin^2(x)\$ D) \$cot^2(x)\$
7	Prove that if tan(θ) = 3 and \$cot(θ) = 1/3\$, then sin(θ) and cos(θ) satisfy the Pythagorean identity.	A) Not satisfied B) Satisfied C) Undefined D) None of the above
8	If tan(θ) = \$3/4\$ and sin(θ) > 0, find the value of cos(θ).	A) \$2/3\$ B) \$3/4\$ C) \$4/3\$ D) 1
9	A ladder leans against a vertical wall. The foot of the ladder is placed 5 meters away from the wall. When the ladder is leaning against the wall, the top of the ladder is 12 meters above the ground. What is the length of the ladder?	A) 10 meters B) 11.25 meters C) 13 meters D) 14.68 meters
10	Find the value of \$tan(60^\circ) + cot(30^\circ)\$ using co-function identities.	A) \$\sqrt(3)\$ B) \$3\sqrt(2)\$ C) \$-3\sqrt(2)\$ D) \$2\sqrt(3)\$

Problem Id

Problem

Options

Find the value of acute angle x, if tan(x) = cot 10°.

A) 40°

B) 70°

C) 80°

D) 60°

Determine the value of cosec 150° using cofunction identities.

A) 1

B) 0

C) undefined

D) 2

If \$ cosθ = 1/4 \$ and \$ cotθ = 2/\sqrt3 \$, what is the value of sinθ ?

A) \$ \sqrt3/4 \$

B) \$ \sqrt3/8 \$

C) \$ \sqrt3/2 \$

D) \$ \sqrt3/18 \$

If cscθ = 0.87 , find \$ sec(θ − pi/2) \$ .

A) 0.87

B) 0.13

C) 0.23

D) 0.77

A wheelchair ramp has an angle of elevation of 45 degrees. If the length of the ramp is 12 meters, find the vertical height gain for someone using the ramp.

A) 12 meters

B) 13 meters

C) 24 meters

D) 15 meters

Simplify the expression \$ (1 - cos(2x))/(sin(2x)) \$.

A) sec(2x)

B) tan(x)

C) \$sin^2(x)\$

D) \$cot^2(x)\$

Prove that if tan(θ) = 3 and \$cot(θ) = 1/3\$, then sin(θ) and cos(θ) satisfy the Pythagorean identity.

A) Not satisfied

B) Satisfied

C) Undefined

D) None of the above

If tan(θ) = \$3/4\$ and sin(θ) > 0, find the value of cos(θ).

A) \$2/3\$

B) \$3/4\$

C) \$4/3\$

D) 1

A ladder leans against a vertical wall. The foot of the ladder is placed 5 meters away from the wall. When the ladder is leaning against the wall, the top of the ladder is 12 meters above the ground. What is the length of the ladder?

A) 10 meters

B) 11.25 meters

C) 13 meters

D) 14.68 meters

Find the value of \$tan(60^\circ) + cot(30^\circ)\$ using co-function identities.

A) \$\sqrt(3)\$

B) \$3\sqrt(2)\$

C) \$-3\sqrt(2)\$

D) \$2\sqrt(3)\$