Answer

Verified

408.9k+ views

**Hint:**There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent. These six trigonometric ratios are abbreviated as $\sin , \cos ,$ tan, $\mathrm{csc},$ sec, cot. These are referred to as ratios since they can be expressed in terms of the sides of a right-angled triangle for a specific angle $\theta$. Trigonometry is defined as the branch of math that deals with calculations related to the sides and angles of triangles.

**Complete step-by-step answer:**The Pythagorean equation relates the sides of a right triangle in a simple way, so that if the

lengths of any two sides are known the length of the third side can be found. Another corollary.

The theorem is that in any right triangle, the hypotenuse is greater than any one of the other sides, but less than their sum.

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. We use special words to describe the sides of right triangles.

Given, $\sin \mathrm{A}=\dfrac{3}{4}$

$\Rightarrow \dfrac{\mathrm{BC}}{\mathrm{AC}}=\dfrac{3}{4}$

$\Rightarrow \mathrm{BC}=3 \mathrm{k}$ and $\mathrm{AC}=4 \mathrm{k}$

where $\mathrm{k}$ is the constant of proportionality. By Pythagoras theorem, we have $\mathrm{AB}^{2}=\mathrm{AC}^{2}-\mathrm{BC}^{2}=(4 \mathrm{k})^{2}-(3 \mathrm{k})^{2}=7 \mathrm{k}^{2}$

$\Rightarrow \mathrm{AB}=\sqrt{7} \mathrm{k}$

$\mathrm{So}, \cos \mathrm{A}=\dfrac{\mathrm{AB}}{\mathrm{AC}}=\dfrac{\sqrt{7} \mathrm{k}}{4 \mathrm{k}}=\dfrac{\sqrt{7}}{4}$

And $\tan \mathrm{A}=\dfrac{\mathrm{BC}}{\mathrm{AB}}=\dfrac{3 \mathrm{k}}{\sqrt{7} \mathrm{k}}=\dfrac{3}{\sqrt{7}}$

**Hence, the correct answer is option B.**

**Note:**The shape of the sine curve is the same for each full rotation of the angle and so the function is called 'periodic'. The period of the function is $360^{\circ}$ or $2 \pi$ radians. We can rotate the point as many times as we like. In mathematical terms we say the 'domain' of the sine function is the set of all real numbers.

The cosine function is a periodic function which is very important in trigonometry. The simplest way to understand the cosine function is to use the unit circle. The $\mathrm{x}$ -coordinate of the point where the other side of the angle intersects the circle is $\cos (\theta),$ and the $y$ -coordinate is $\sin (\theta)$.

Recently Updated Pages

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

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

One cusec is equal to how many liters class 8 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

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

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

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