Answer:
76.57295824...
Step-by-step explanation:
1. tan Ø =4/3pi
2.( tan^-1)tan Ø =4/3pi(tan^-1)
-Multiply by 2nd tan or tan to the negative first power on both sides
3. Answer = 76.8 (rounded to the nearest tenths)
Answer:
cos 2Ф = [tex]\frac{-7}{25}[/tex]
Step-by-step explanation:
From the question above, we are ask to find cos 2Ф
To solve this problem, we need to first know what formula to use.
Using multiple formula;
cos 2Ф = cos²Ф - sin²Ф
since tan Ф is given as 4/3, then we need to first find sin Ф and cos Ф
tan Ф = [tex]\frac{4}{3}[/tex] = [tex]\frac{opp}{adj}[/tex]
from the above, opposite = 4 adjacent =3
hypotenuse = ?
we need to find the hypotenuse
Let hyp = x
using Pythagoras theorem,
hyp² = opp² + adj²
= 4² + 3²
=16 + 9
= 25
hyp = √25
hyp = 5
opposite = 4 adjacent = 3 hypotenuse= 5
sinФ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]
cos Ф = [tex]\frac{adjacent}{hypotenus}[/tex] =[tex]\frac{3}{5}[/tex]
cos 2Ф = cos²Ф - sin²Ф
= [tex](\frac{3}{5} )^{2}[/tex] - [tex](\frac{4}{5}) ^{2}[/tex]
cos 2Ф = [tex]\frac{9}{25}[/tex] - [tex]\frac{16}{25}[/tex]
cos 2Ф = [tex]\frac{-7}{25}[/tex]
