Lesson Example Discussion Quiz: Class Homework |
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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