The graphs of all 6 trigonometric functions are given below in a random order. They are not labeled since you are expected to know which trigonometric function corresponds to each graph.

Click the magnifying glass icon in the lower-right corner of any graph to view an enlarged version of it. This will help make the scaling on the horizontal axis easier to read. When viewing an enlarged graph, you can click and drag the lower-right corner to increase or decrease the size of the viewing window.

123-1-2-3π/6π/3π/22π/35π/6π7π/64π/33π/25π/311π/62π13π/6

123-1-2-3π/6π/3π/22π/35π/6π7π/64π/33π/25π/311π/62π13π/6

1-1π/6π/3π/22π/35π/6π7π/64π/33π/25π/311π/62π13π/6

1-1π/6π/3π/22π/35π/6π7π/64π/33π/25π/311π/62π13π/6

123-1-2-3π/6π/3π/22π/35π/6π7π/64π/33π/25π/311π/62π13π/6

123-1-2-3π/6π/3π/22π/35π/6π7π/64π/33π/25π/311π/62π13π/6

In parts (a) and (b) below, you must select ALL of the correct answers without selecting any incorrect answer choices (i.e. each part is graded as "all-or-nothing").

(a) Use the graph of f(t)=sec⁡(t)\displaystyle {f{{\left({t}\right)}}}={\sec{{\left({t}\right)}}} to find the values of t\displaystyle {t} in the interval [0,2π)\displaystyle {\left[{0},{2}\pi\right)} that satisfy the equation:

sec⁡t=2\displaystyle {\sec{{t}}}=\sqrt{{{2}}}
(FYI: 2≈1.414\displaystyle \sqrt{{{2}}}\approx{1.414})

(b) Use the graph of f(t)=cos⁡(t)\displaystyle {f{{\left({t}\right)}}}={\cos{{\left({t}\right)}}} to find the values of t\displaystyle {t} in the interval [0,2π)\displaystyle {\left[{0},{2}\pi\right)} that satisfy the equation:

cos⁡t=−12\displaystyle {\cos{{t}}}=-\frac{{1}}{{2}}


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