Answer

Verified

406.8k+ views

**Hint:**Sin is comparable to the side inverse a given point in a correct triangle to the hypotenuse. Cos is identical to the proportion of the side nearby an intense point in a right-calculated triangle to the hypotenuse.

**Complete step by step answer:**

Use the definition of cosine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

$\cos (x) = \dfrac{{adjacent}}{{hypotenuse}}$

Let's find the opposite side of the unit circle triangle. Since the adjacent side and hypotenuse are known, use the Pythagorean theorem to find the remaining side.

$opposite = \sqrt {hypotenuse{e^2} - adjacent{t^2}} $

Replace the known value of the in the equation.

$opposite = \sqrt {{{13}^2} - {{12}^2}} $

Simplify $\sqrt {{{13}^2} - {{12}^2}} $

Raise 13 to the power of 2.

$Opposite = \sqrt {169 - {{(12)}^2}} $

Raise 12 to the power of 2.

$Opposite = \sqrt {169 - 1.144} $

Multiply $ - 1$ by 144

$Opposite = \sqrt {169 - 144} $

Subtract 144 from 169.

$Opposite = \sqrt {25} $

Rewrite 25 as ${5^2}$.

$Opposite = \sqrt {{5^2}} $

Pull terms out from under the radical, assuming positive real numbers.

$Opposite = 5$

Use the definition of $\sin $to find the value of $\sin (x)$.

$\sin (x) = \dfrac{{opp}}{{hyp}}$

Substitute in the known values.

$\sin (a) = \dfrac{5}{{13}}$.

$cos(a) = \dfrac{{12}}{{13}}$. Angle is in either 1st quadrant or in the 4th.

$\sin (a) = \pm \dfrac{5}{{13}}$. As, $\sin (a) < 0$, a is in the 4th quadrant. So, $\sin (a) = - \dfrac{5}{{13}}$.

Use the definition of tangent to find the value of $\tan (x)$

$\tan (x) = \dfrac{{opp}}{{adj}}$

Substitute in the known values.

$\tan (a) = - \dfrac{5}{{12}}$.

**Thus, the ratio of $\dfrac{{\sin (a)}}{{\cos (a)}} = \tan (a) = - \dfrac{5}{{12}}$.**

**Note:**We note that the domain of sin inverse function is $( - 1,1)$ and since $\dfrac{{12}}{{13}} \in ( - 1,1)$ the value $\sin = - \dfrac{5}{{13}}$ is well defined.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE