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3 years ago

Anyone know how to do trig? Given tan Ф = 4/5, find all other trig functions.

Mathematics

1 answer:

mars1129 [50]3 years ago

7 0

9514 1404 393

Answer:

sin(Ф) = (4/41)√41; csc(Ф) = (√41)/4
cos(Ф) = (5/41)√41; sec(Ф) = (√41)/5
tan(Ф) = 4/5; cot(Ф) = 5/4

Step-by-step explanation:

The mnemonic SOH CAH TOA can help you with three of the functions. Then you need to remember the relations between those and the other three.

Tan = Opposite/Adjacent

tan(Ф) = 4/5

This suggests you can draw a triangle like the one attached that has adjacent side 5 and opposite side 4. Then hypotenuse can be found from the Pythagorean theorem:

AC² = AB² +BC² = 5² +4² = 41

AC = √41 . . . . . hypotenuse

Then the other trig functions are ...

Sin = Opposite/Hypotenuse

sin(Ф) = 4/√41 = (4/41)√41

Cos = Adjacent/Hypotenuse

cos(Ф) = 5/√41 = (5/41)√41

And the reciprocal functions are ...

csc(Ф) = 1/sin(Ф) = (√41)/4

sec(Ф) = 1/cos(Ф) = (√41)/5

cot(Ф) = 1/tan(Ф) = 5/4

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