Unformatted text preview: shall see in the sections to come, many applications in
trigonometry involve ﬁnding the measures of the angles in, and lengths of the sides of, right triangles.
Indeed, we made good use of some properties of right triangles to ﬁnd the exact values of the cosine
and sine of many of the angles in Example 10.2.1, so the following development shouldn’t be that
much of a surprise. Consider the generic right triangle below with corresponding acute angle θ.
The side with length a is called the side of the triangle adjacent to θ; the side with length b is
called the side of the triangle opposite θ; and the remaining side of length c (the side opposite the
right angle) is called the hypotenuse. We now imagine drawing this triangle in Quadrant I so that
the angle θ is in standard position with the adjacent side to θ lying along the positive x-axis.
If the object does not start at (r, 0) when t = 0, the equations of motion need to be adjusted accordingly. If
t0 > 0 is the ﬁrst time the object passes through the point (...
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