SaiBook.us SAT-3

Lesson Example Discussion Quiz: Class Homework

Quiz In Class

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: in Class

Problem Id	Problem	Options
1	A person, standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank is 60°. when he retreats 20m from the bank, he finds the angle to be 30°. The height of the tree and the breadth of the river.	A) h = 10 m and w = 17.32 m B) h = 17.32 m and w = 10 m C) h = 10 m and w = 13.32 m D) h = 13.32 m and w = 10 m
2	Solve for x in the interval (0,2π): \$ cos(x)/(1 + sin(x)) = 1/\sqrt3 \$.	A) \$ x = pi/2\$ B) \$ x = (3pi)/4 \$ C) \$x = pi/6\$ D) \$ x = (5pi)/3 \$
3	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) \$ 53/56 \$ C) \$ 36/65 \$ D) \$ 61/65 \$
4	Triangle ABC is similar to triangle DEF, where A corresponds to D and C corresponds to F. Angles C and F are right angles. If \$tan(A) = sqrt\3\$ and DF = 125, what is the length of stem[\bar(DE)]?	A) \$125\sqrt(3)\$ B) \$(125)sqrt3/3\$ C) \$(125)sqrt3/2\$ D) 250
5	Prove the identity: \$cos(x)/(1+sin(x)) = sec(x) - tan(x)\$	A) Not proved B) Infinity C) Proved D) 0
6	If 3 cot A = 4, check whether \$(1 – tan^2(A))/(1 + tan^2(A))\$ = \$cos^2 (A) – sin^2 (A)\$.	A) 0 B) 1 C) Not proved D) Proved
7	A satellite dish is designed to pick up signals from a satellite directly above the Earth’s equator. The dish is positioned at a location where the latitude is 30 degrees north. If the dish needs to be angled such that the signal from the satellite reaches the dish at an angle θ to the vertical, express the angle θ in terms of trigonometric identities.	A) \$30^∘\$ B) \$60^∘\$ C) \$55^∘\$ D) \$90^∘\$
8	A kite is attached to a string that is 200 feet long. If the string makes an angle of 40° with the ground, how high is the kite?	A) 128.4 ft B) 182.4 ft C) 184.2 ft D) 124.8 ft
9	If \$5(tan^2 x - cos^2 x) = 2cos 2x + 9\$, then the value of cos4x is:	A) \$9/7\$ B) \$ 7/9\$ C) \$- 9/7\$ D) \$- 7/9\$
10	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) \$- sec^2(θ)\$ D) \$- csc^2(θ)\$

Problem Id

Problem

Options

A person, standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank is 60°. when he retreats 20m from the bank, he finds the angle to be 30°. The height of the tree and the breadth of the river.

A) h = 10 m and w = 17.32 m

B) h = 17.32 m and w = 10 m

C) h = 10 m and w = 13.32 m

D) h = 13.32 m and w = 10 m

Solve for x in the interval (0,2π): \$ cos(x)/(1 + sin(x)) = 1/\sqrt3 \$.

A) \$ x = pi/2\$

B) \$ x = (3pi)/4 \$

C) \$x = pi/6\$

D) \$ x = (5pi)/3 \$

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) \$ 53/56 \$

C) \$ 36/65 \$

D) \$ 61/65 \$

Triangle ABC is similar to triangle DEF, where A corresponds to D and C corresponds to F. Angles C and F are right angles. If \$tan(A) = sqrt\3\$ and DF = 125, what is the length of stem[\bar(DE)]?

A) \$125\sqrt(3)\$

B) \$(125)sqrt3/3\$

C) \$(125)sqrt3/2\$

D) 250

Prove the identity:
\$cos(x)/(1+sin(x)) = sec(x) - tan(x)\$

A) Not proved

B) Infinity

C) Proved

D) 0

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

A) 0

B) 1

C) Not proved

D) Proved

A satellite dish is designed to pick up signals from a satellite directly above the Earth’s equator. The dish is positioned at a location where the latitude is 30 degrees north. If the dish needs to be angled such that the signal from the satellite reaches the dish at an angle θ to the vertical, express the angle θ in terms of trigonometric identities.

A) \$30^∘\$

B) \$60^∘\$

C) \$55^∘\$

D) \$90^∘\$

A kite is attached to a string that is 200 feet long. If the string makes an angle of 40° with the ground, how high is the kite?

A) 128.4 ft

B) 182.4 ft

C) 184.2 ft

D) 124.8 ft

If \$5(tan^2 x - cos^2 x) = 2cos 2x + 9\$, then the value of cos4x is:

A) \$9/7\$

B) \$ 7/9\$

C) \$- 9/7\$

D) \$- 7/9\$

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) \$- sec^2(θ)\$

D) \$- csc^2(θ)\$