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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.

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,
b = 5 - 2
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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Janet Yang


I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.


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