Unformatted text preview: skip the ‘angle’ argument in number 3 as we did in
number 2 in Example 10.6.7 above. It is true that one solution to cos(x) = − 3 is x = arccos − 3
and since the period of the cosine function is 2π , we can readily express one family of solutions
as x = arccos − 5 + 2πk for integers k . The problem with this is that there is another family
of solutions. While expressing this family of solutions in terms of arccos − 5 isn’t impossible, it
13 In general, equations involving cosine and
certainly isn’t as intuitive as using a reference angle.
sine (and hence secant or cosecant) are usually best handled using the reference angle idea thinking
geometrically to get the solutions which lie in the fundamental period [0, 2π ) and then add integer
multiples of the period 2π to generate all of the coterminal answers and capture all of the solutions.
With tangent and cotangent, we can ignore the angular roots of trigonometry altogether, invoke
the appropriate inverse function, and then add integer multip...
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