Milestone One: First Practice Problem Walkthrough: Case Study

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MAT 140 Milestone One: First Practice Problem Walkthrough
Anthony Martinez
Southern New Hampshire University Given the following right triangle, find cosθ, sinθ, tanθ, secθ, cscθ, and cotθ. Do not approximate: Find exact answers. Show all of your work and explain steps as necessary. The first step before we begin defining the functions of the right triangle above would be to establish the labels of just what each variable is. First, 7 = The Hypotenuse, which is defined as the longest side of the right triangle and is the side opposite the right angle. Second is 4 = The Opposite Side, which consists of the side that is opposite to the given angle, or in this case variable θ (theta). Next, is a = The Adjacent Side which can be explained …show more content…
Which in term would conclude that Cosθ = √33/17 .
Sinθ [Sine]: The sine of an angle is determined per the ratio of the side opposite to the angle over the hypotenuse. This relationship of the triangle to the theta is demonstrated through Sinθ = (Opposite Side)/Hypotenuse Which, would determine that in the above triangle Sinθ = 4/7 .
Tanθ [Tangent]: This includes the ratio of the side opposite the angle, including the angle over the side as well as the adjacent side. This relationship can is shown through the function Tanθ = (Opposite Side)/(Adjacent Side) . The adjacent side when Cosθ was calculated, = √33, which would determine, Tanθ = 4/√33.
Secθ [Secant]: This would be defined as the reciprocal of cosine. The relationship Secθ of the sides to the triangle to the theta can be considered through Secθ = Hypotenuse/(Adjacent Side) . this would then show, Secθ = 7/√33.
Cscθ [Cosecant]: Cosecant would be the reciprocal of sine. In the case of Cscθ, the relationship of the sides of the triangle to theta is demonstrated through; Cscθ = Hypotenuse/(Opposite Side) . This in turn would mean, Cscθ = 7/4
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