Quiz In Class

Title: Trigonometry Identities (quotient , co-function)

Grade: 1400-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

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) \$90^∘\$

C) \$60^∘\$

D) \$55^∘\$

2

Simplify \$ 3sin^3(t) csct + cos^2(t) + 2cos(−t)cost\$.

A) 1

B) 2

C) 4

D) 3

3

Simplify \$ (sin2theta)/(1 + cos2theta) * cot^2theta\$.

A) \$tan \theta\$

B) \$cot \theta\$

C) \$csc \theta\$

D) \$sec \theta\$

4

Prove the identity: \$ (sin(x) + cos(x))/(cos(x) - sin(x)) = tan( x + pi/4)\$.

A) Proved

B) Zero

C) Not Proved

D) Infinity

5

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

A) \$ x = pi/6 \$

B) \$ x = pi/2\$

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

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

6

Find the value of θ if \$tan θ = cot (θ/2 + π/8) \$ using cofunction identities.

A) \$ θ = (5pi)/2\$

B) \$ θ = (pi)/4\$

C) \$ θ = (pi)/8\$

D) \$ θ = (2pi)/3\$

7

A street light is mounted on a pole that is 8 meters high. The light casts a shadow of a nearby building such that the angle of elevation from the end of the shadow to the top of the pole is 60°. Determine the distance from the pole to the end of the shadow using the co-function identity for sine and cosine.

A) 6 m

B) 4 m

C) 7 m

D) 5 m

8

Evaluate \$ (1 + cos θ - sin^2(θ)) /(sin(θ) ( 1 + cos(θ)))\$.

A) sec(θ)

B) tan(θ)

C) cot(θ)

D) sin(θ)

9

A pilot is flying at a constant altitude and needs to determine the distance to a nearby airport. The pilot measures the angle of depression to the airport as 70 degrees. If the altitude of the plane is 5 kilometers, find the horizontal distance to the airport.

A) 1.28 km

B) 2.747 km

C) 1.82 km

D) 2.477 km

10

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

A) Zero

B) Not proved

C) Infinity

D) Proved


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