SaiBook.us SAT-3

Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Trignometry

Grade: Top-SAT3 Lesson: S7-P1

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	If sin(α) = 0.5 and cos(β) = 0.8, find the values of sin(α + β) and cos(α - β).	A) 0.7296 and 0.7231 B) 0.9236 and 0.9729 C) 0.8996 and 0.9890 D) 0.9196 and 0.9928
2	Triangle KLM is similar to triangle QRS, where angle K corresponds to angle Q and where angles L and R are right angles. If \$ sin K = 105/233 \$ and \$ sin M = 208/233 \$.what is the value of tan S?	A) 1.99 B) 1.98 C) 1.93 D) 1.91
3	Simplify the following expression: \$ cot^2(θ) - csc^2(θ) / (1 + cot(θ)tan(θ)) \$	A) \$ 2/3 \$ B) \$ - 1/2 \$ C) \$ 4/3 \$ D) \$ 1/2 \$
4	A person standing 10 meters away from the base of a building observes that the angle of elevation to the top of the building is 60°. At the same time, another person standing on the roof of the buliding observes that the angle of depression to the first person is 45°.Find the height of the buliding.	A) 11 meters B) 12 meters C) 10 meters D) 15 meters
5	Given the Pythagorean Identity: \$ sin^2(x) + cos^2(x) = 1 \$, prove the Double Angle Identity for Cosine: \$ cos(2x) = cos^2(x) − sin^2(x) \$.	A) Proved B) Infinity C) Inconclusive D) Not Proved
6	A lighthouse is located on a cliff 80 meters above sea level. It emits a beam of light that rotates at a constant rate, making a full revolution every 30 seconds. A ship is sailing directly towards the cliff at a constant speed of 10 meters per second. How fast is the distance between the ship and the lighthouse decreasing when the ship is 100 meters away from the cliff?	A) \$9.42 "meter"/ "second"\$ B) \$- 4.92 "meter"/ "second"\$ C) \$4.92 "meter"/ "second"\$ D) \$- 9.42 "meter"/ "second"\$
7	In a certain triangle, the measures of ∠A and ∠B are (6k - 8)° and (7k - 45)°, respectively. If \$((sin ∠A) /(cos ∠B)) = 1\$, what is the value of k?	A) 11 B) 28 C) 6 D) 18
8	(1 + cos α)(1 + cos β)(1 + cos γ) = (1 – cos α)(1 – cos β)(1 – cos γ). What are the possible values for each member of the equation?	A) 0 B) cos α + cos β + cos γ C) \$ 1 + cos^2(β)cos^2(γ) \$ D) sin α sin β sin γ
9	Prove the identity \$sec(θ) − cos(θ) = sin(θ)/sin(θ + π/2)\$.	A) Not proved B) proved C) 0 D) None of these above
10	Prove the quotient identity: \$(cos^2 (θ)/(1 - sin(θ))) + ((1 - sin(θ))/(cos^2 (θ))) = sec^2 (θ)\$.	A) \$LHS ne RHS\$ B) LHS = Infinity C) LHS = RHS D) None of these above

Problem Id

Problem

Options

If sin(α) = 0.5 and cos(β) = 0.8, find the values of sin(α + β) and cos(α - β).

A) 0.7296 and 0.7231

B) 0.9236 and 0.9729

C) 0.8996 and 0.9890

D) 0.9196 and 0.9928

Triangle KLM is similar to triangle QRS, where angle K corresponds to angle Q and where angles L and R are right angles. If \$ sin K = 105/233 \$ and \$ sin M = 208/233 \$.what is the value of tan S?

A) 1.99

B) 1.98

C) 1.93

D) 1.91

Simplify the following expression:

\$ cot^2(θ) - csc^2(θ) / (1 + cot(θ)tan(θ)) \$

A) \$ 2/3 \$

B) \$ - 1/2 \$

C) \$ 4/3 \$

D) \$ 1/2 \$

A person standing 10 meters away from the base of a building observes that the angle of elevation to the top of the building is 60°. At the same time, another person standing on the roof of the buliding observes that the angle of depression to the first person is 45°.Find the height of the buliding.

A) 11 meters

B) 12 meters

C) 10 meters

D) 15 meters

Given the Pythagorean Identity: \$ sin^2(x) + cos^2(x) = 1 \$, prove the Double Angle Identity for Cosine: \$ cos(2x) = cos^2(x) − sin^2(x) \$.

A) Proved

B) Infinity

C) Inconclusive

D) Not Proved

A lighthouse is located on a cliff 80 meters above sea level. It emits a beam of light that rotates at a constant rate, making a full revolution every 30 seconds. A ship is sailing directly towards the cliff at a constant speed of 10 meters per second. How fast is the distance between the ship and the lighthouse decreasing when the ship is 100 meters away from the cliff?

A) \$9.42 "meter"/ "second"\$

B) \$- 4.92 "meter"/ "second"\$

C) \$4.92 "meter"/ "second"\$

D) \$- 9.42 "meter"/ "second"\$

In a certain triangle, the measures of ∠A and ∠B are (6k - 8)° and (7k - 45)°, respectively. If \$((sin ∠A) /(cos ∠B)) = 1\$, what is the value of k?

A) 11

B) 28

C) 6

D) 18

(1 + cos α)(1 + cos β)(1 + cos γ) = (1 – cos α)(1 – cos β)(1 – cos γ).
What are the possible values for each member of the equation?

A) 0

B) cos α + cos β + cos γ

C) \$ 1 + cos^2(β)cos^2(γ) \$

D) sin α sin β sin γ

Prove the identity \$sec(θ) − cos(θ) = sin(θ)/sin(θ + π/2)\$.

A) Not proved

B) proved

C) 0

D) None of these above

Prove the quotient identity:
\$(cos^2 (θ)/(1 - sin(θ))) + ((1 - sin(θ))/(cos^2 (θ))) = sec^2 (θ)\$.

A) \$LHS ne RHS\$

B) LHS = Infinity

C) LHS = RHS

D) None of these above