trigonometry

Question

Sketch a triangle with a hypotenuse square root of 193 and legs 12 and 7 units. Find the six trigonometric function values of the smallest angle theta. 

Answer 1

First of all, remember that the smallest side is opposite the smallest angle, so the smallest angle is the one whose opposite side is 7.  That means that the adjacent side for this angle is the other leg, 12.

 

Next, remember SOHCAHTOA

 

Sin θ = Opposite / Hypotenuse = 7 / √193 = 0.5039

Cos θ = Adjacent / Hypotenuse = 12 / √193 = 0.8638

Tan θ = Opposite / Adjacent = 7 / 12 = 0.5833

 

Finally, remember that the other three functions are just reciprocals of the first three.  Reciprocal means 1 divided by the number, or do the division with the numerator and denominator reversed.

 

sec θ = 1 / cos θ = √193 / 12 = 1.1577

csc θ = 1 / sin θ = √193 /7 = 1.9846

cot θ = 1 / tan θ = 12 / 7 = 1.7143