Answer

Verified

375k+ 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

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Name 10 Living and Non living things class 9 biology CBSE

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

List some examples of Rabi and Kharif crops class 8 biology CBSE

Write the 6 fundamental rights of India and explain in detail