Question 802600
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I could use a little help with this math question for my ACT prep worksheets I've been working on. It is question
433 in my booklet:
Using a right triangle with an acute angle theta, find the other five trigonometric functions of theta if
cos theta = 2/5 I am told not to use decimals in my answer.

I was hoping you could show me the answer and sort of a guide/process of how you got it, so I can be sure to really 
learn from it and make sure I "get it down" for future similar questions. Thank you for taking the time to answer
my question, Reggie
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{{{cos (theta) = 2/5 = A/H = x/r}}}
{{{y^2 = r^2 - x^2}}} ===> {{{y^2 = 5^2 - 2^2}}} ===> {{{y^2 = 25 - 4}}} ===> {{{y^2 = 21}}} ===> {{{y = sqrt(21)}}} 
x = 2    ;    r = 5     ;     {{{y = sqrt(21)}}}   
<pre>{{{highlight_green(matrix(3,7, cos (theta), "=", A/H, "=", x/r, "=", 2/5, highlight(sin (theta)), "=", O/H, "=", y/r, "=", highlight(sqrt(21)/5), highlight(tan (theta)), "=", O/A, "=", y/x, "=", highlight(sqrt(21)/2)))}}}       {{{highlight_green(matrix(3,7, highlight(sec (theta)), "=", H/A, "=", r/x, "=", highlight(5/2), highlight(csc (theta)), "=", H/O, "=", r/y, "=", 5/sqrt(21) = highlight(5sqrt(21)/21), highlight(cot (theta)), "=", A/O, "=", x/y, "=", 2/sqrt(21) = highlight(2sqrt(21)/21)))}}}</font></font></font></b></pre></pre></pre>