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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

Draw a right triangle with base angle of θ, adjacent side of length 2, and hypotenuse of length 5.

http://www.flickr.com/photos/dwread/10461400016/

The actual triangle probably isn't this size, but it doesn't matter. Trigonometry is about the ratios between the sides.

By the Pythagorean Theorem,

b² = 5² - 2²

b = √21

sinθ = (√21)/5

tanθ = (√21)/2

secθ = 1/cosθ = 5/2

cscθ = 1/sinθ = 5/√21 = (5√21)/21

cotθ = 1/tanθ = 2/√21 = (2√21)/21

Since you aren't supposed to use decimals, leave the answers in fraction form.

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