Question

If sinA=3/4 find the values of other trigonometry ratios

Answer 1

Answer:

I hope it would help you

Answer 2

Assumption

∆PQR be an right angled triangle at Q

Given

$\tt{\rightarrow sinA=\dfrac{3}{4}}$

As we know that :-

$\tt{\rightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}}$

$\tt{\rightarrow sinP=\dfrac{QR}{PR}}$

$\tt{\rightarrow\dfrac{QR}{PR}=\dfrac{3}{4}}$

QR = 3x

Also

PR = 4x (For any positive number x)

Therefore

PQ² = PR² - QR²

= (4x)² - (3x)²

= 16x² - 9x²

= 7x²

PQ = √7x

$\tt{\rightarrow cosA=\dfrac{PQ}{PR}}$

$\tt{\rightarrow cosA=\dfrac{\sqrt{7}x}{4x}}$

$\tt{\rightarrow cosA=\dfrac{\sqrt{7}}{4}}$

Now,

$\tt{\rightarrow tanA=\dfrac{QR}{PQ}}$

$\tt{\rightarrow tanA=\dfrac{3x}{\sqrt{7}x}}$

$\tt{\rightarrow tanA=\dfrac{3}{\sqrt{7}}}$

$\tt{\rightarrow tanA=\dfrac{3\sqrt{7}}{7}}$

Now,

$\tt{\rightarrow cosecA=\dfrac{4}{3}}$

$\tt{\rightarrow secA=\dfrac{4}{\sqrt{7}}\;or\;\dfrac{4\sqrt{7}}{7}}$

$\tt{\rightarrow cotA=\dfrac{\sqrt{7}}{3}}$

$\boxed{\begin{minipage}{11 cm} Fundamental Trignometric Indentities \\ \\ \sin^{2}\theta+\cos^{2}\theta =1 \\ \\ 1+tan^{2}\theta=\sec^{2}\theta \\ \\ 1 + cot^{2}\theta=\text{cosec}^2\theta \\ \\ tan\theta =\dfrac{sin\theta}{cos\theta} \\ \\ cot\theta =\dfrac{cos\theta}{sin\theta} \end{minipage}}$