SOLUTION: HELLO! I need help! Match each trig function with its correct value if θ is an acute angle and cscθ = 2 1/2 1. sqroot 21/5 2. sqroot 21/2 3. 5sqroot21/21 4. 2/5

Algebra ->  Trigonometry-basics -> SOLUTION: HELLO! I need help! Match each trig function with its correct value if θ is an acute angle and cscθ = 2 1/2 1. sqroot 21/5 2. sqroot 21/2 3. 5sqroot21/21 4. 2/5       Log On


   



Question 891554: HELLO! I need help!
Match each trig function with its correct value if θ is an acute angle and cscθ = 2 1/2
1. sqroot 21/5
2. sqroot 21/2
3. 5sqroot21/21
4. 2/5
5. 2sqroot21/21

a. sinx
b. cotx
c. cosx
d. tanx
3. secx

Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!
csc%28theta%29%22%22=%22%222%261%2F2

Change 2%261%2F2 to an improper fraction:

csc%28theta%29%22%22=%22%225%2F2

Since cosecant=hypotenuse%2Fopposite we draw a right
triangle with an angle theta with a hypotenuse of 5, which is 
the same as the numerator of the fraction 5%2F2, and with 
a side opposite angle theta of 2, which is the denominator
of the fraction 5%2F2.



[You don't have to be accurate with your drawing, just any sketch of
a right triangle will do.]

Next we use the Pythagorean theorem to calculate the adjacent side
to angle theta:

adjacent%5E2%2Bopposite%5E2=hypotenuse%5E2

adjacent%5E2%2B2%5E2=5%5E2

adjacent%5E2%2B4=25

adjacent%5E2=21

adjacent=sqrt%2821%29

So we label the adjacent side as sqrt%2821%29



sin%28theta%29=opposite%2Fhypotenuse=2%2F5

cos%28theta%29=adjacent%2Fhypotenuse=sqrt%2821%29%2F5



cot%28theta%29=adjacent%2Fopposite=sqrt%2821%29%2F2



Edwin