Trigonometry Problems and Solutions (Math Problem Sample)

Math Questions: Trigonometry
Student’s Name
Institutional Affiliation
Question
Solution
11620504762500
1035050514350011620503302000
312420016129000S
10 Feet
1026160889000
466121720478800
4676775825500
a
θ
Fig 1
With the consideration of angle θ, the side represented as 10 feet is the “opposite”, the side labelled ‘S’ the “Hypotenuse” and side ‘a’ as the “Adjacent”. These terms will be used in the solution of the trigonometric problem.
* Write θ as a function of S.
Solution
According to trigonometric functions and identities, the values of any angle or side can be determined by the existing relational computations of the established rules. For instance, the provided question requires one to find the expression of θ as a function of S. To solve the expression, one has to first identify what each aspect in the correlation represents.
* Θ represents the angle between the water level on which the boat is located and the level of the dock on which the winch is located.
* S represents the distance between the boat and the winch along the rope or chain that will be used to reel in the boat while docking.
To find the relationship between angle θ and the distance S (writing θ as a function of S), there is need to identify the trigonometric relations between an angle and a side on a right angled triangle.
The diagram above represents a simplified model of the boat docking question. The hypotenuse is the distance S, which is the distance between the winch and the boat along the chain or rope used to tow the boat in while docking. Angle θ on the other hand represents the angle between the chain, and the water level of the boat.
* To find angle θ;
We are provided with the value of the Opposite side as 10 feet, and the value of the Hypotenuse as S.
The relational function is:
sinθ=Opposite Hypotenuse … (i)
Hence,
* Opposite = 10 fe