Question

Given tan theta=4/3 and pi

Answer 1

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 2

Answer:

cos 2Ф =  $\frac{-7}{25}$

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 =  $\frac{4}{3}$  = $\frac{opp}{adj}$

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 =   $\frac{opposite}{hypotenuse}$     =   $\frac{4}{5}$

cos Ф  =  $\frac{adjacent}{hypotenus}$  =$\frac{3}{5}$

cos 2Ф = cos²Ф  - sin²Ф

 

             = $(\frac{3}{5} )^{2}$    -     $(\frac{4}{5}) ^{2}$

cos 2Ф    =  $\frac{9}{25}$   -      $\frac{16}{25}$

cos 2Ф      =  $\frac{-7}{25}$