SOLUTION: Explain (suggested length 1–2 paragraphs) how the functions and definitions in parts A1 and A2 are related by investigating a right triangle inscribed in a unit circle. Refer to th

Algebra ->  Circles -> SOLUTION: Explain (suggested length 1–2 paragraphs) how the functions and definitions in parts A1 and A2 are related by investigating a right triangle inscribed in a unit circle. Refer to th      Log On


   

Question 564699: Explain (suggested length 1–2 paragraphs) how the functions and definitions in parts A1 and A2 are related by investigating a right triangle inscribed in a unit circle. Refer to the diagrams in parts A1 and A2 as necessary.
a. Explain how you remember the relationships among these trigonometric functions.
part a1 refers to the right triangle definitions in this completed chart
part a2 refers to the unit circle definitions


Function Right Triangle Definition Unit Circle Definition
Sine Opposite/hypotenuse Sin (ang+ 2 pi k)
Cosine Adjacent/hypotenuse Cos (ang+ 2 pi k)
Tangent Opposite/adjacent Sin/cos
Cosecant Hypotenuse/side opposite acute angle
Reciprocal of sine 1/sin
Secant Hypotenuse/short side adjacent to acute angle
Reciprocal of cosine 1/cos
Cotangent Side adjacent to acute angle/side opposite angle 1/tan or sin/cos
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
You didn't provide any diagrams. I think you are referring to a triangle that looks something like this:



Suppose that this triangle is part of the unit circle with radius 1 and origin O(0,0). Then




Other trig functions (tan, csc, etc.) should follow. Note that b and a are simply the x- and y-coordinates of a point on the unit circle.