SOLUTION: 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 the

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Question 802600: 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
Found 2 solutions by lwsshak3, MathTherapy:
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Using a right triangle with an acute angle theta, find the other five trigonometric functions of theta if cos theta = 2/5
***
use x for theta
Identity: sin^2x+cos^2x=1
sin^2x=1-cos^2x
take sqrt of both sides
sinx=√(1-cos^2x)
sinx=√(1-(2/5)^2)
=√(1-4/25)
=√(25/25-4/25)
=√(21/25)
sinx=√21/5
..
cosx=2/5(given)
sinx=√21/5
tanx=sinx/cosx=√21/2
secx=1/cosx=5/2
cscx=1/sinx=5/√21=5√21/21
cotx=1/tanx=2/√21=2√21/21

Answer by MathTherapy(10839) (Show Source):
You can put this solution on YOUR website!

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 ******************* ===> ===> ===> ===> x = 2 ; r = 5 ;