Question

What’s the value of
tan (3arc cos 3/4)

Answer 1

`tan(3 * arc \ cos((3)/(4) ))=(√(7) )/(3)`

Explanation:

The given expression is

`tan(3 * arc \ cos((3)/(4) ))`

Where

`cos^(-1)((3)/(4) )=x\\`, which means that,
`cosx=(3)/(4)`

If we analyse this trigonometric reason in a right triangle, we would find the hypothenuses is 4 and the adjacent leg is 3. Then, using pythagorean theorem, we find the other leg

`y^(2)=4^(2) -3^(2)\\ y=√(16-9)=√(7)`

Which means the opposite leg of our right triangle is the square root of seven.

Finally, using such right triangle, we find the tangent reason, which is the quotient between the opposite leg and the adjacent leg

`tan(radian \ value)=(√(7) )/(3)`

Therefore, the answer is
`(√(7) )/(3)`

Answer 2

Answer: -1.469

This trigonometric function can be written as:

`tan (3 cos^(-1) ((3)/(4)))` (1)

Firstly, we have to solve the inner parenthesis:

`cos^(-1) ((3)/(4))= 41.409` (2)

Substituting (2) in (1):

`tan (3(41.409))=tan(124.228)` (4)

Finally we obtain the value:

`tan(124.228)=-1.469`