Question

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

Answer 1

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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