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levacccp [35]
2 years ago
9

Given tan theta=4/3 and pi

Mathematics
2 answers:
natima [27]2 years ago
4 0

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)

VLD [36.1K]2 years ago
4 0

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}

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