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bixtya [17]
3 years ago
9

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

Mathematics
2 answers:
Volgvan3 years ago
6 0
<h2>Answer: -1.469</h2>

This trigonometric function can be written as:

tan (3 cos^{-1} (\frac{3}{4}))   (1)

Firstly, we have to solve the inner parenthesis:

cos^{-1} (\frac{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  

Marat540 [252]3 years ago
5 0

Answer:

tan(3 \times arc \ cos(\frac{3}{4} ))=\frac{\sqrt{7} }{3}

Step-by-step explanation:

The given expression is

tan(3 \times arc \ cos(\frac{3}{4} ))

Where

cos^{-1}(\frac{3}{4} )=x\\, which means that, cosx=\frac{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=\sqrt{16-9}=\sqrt{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)=\frac{\sqrt{7} }{3}

Therefore, the answer is \frac{\sqrt{7} }{3}

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