Question

if 4 sin o = 3 cos o, find cos o​

Answer 1

Solution:-

Given,

• 4 sin o=3 cos o

Therefore, sin o=3/4 cos o

And cos o=4/3 sin o

We know,

tan o= sin o/cos o

= (3/4 cos o) / cos o

=3/4

but tan o= perpendicular/base

let the perpendicular and bade=3x and 4x respectively

Therefore we got

• perpendicular=3
• base= 4

Using Pythagorean theorem....

hypotenuse^2 = base^2+height^2

= (4)^2 + (3)^2

= 16 + 9

= 25

We got, hypotenus= √(25) =5

Now, sin o = height/hypotenus

= 3/5

cos o=4/3 sin o [As mentioned in the beginning]

•°• cos o= 4/3×3/5

= 4/5

Correct Answer:-

• sin o= 3/5
• cos o= 4/5

Answer 2

Given:-

• 4 sin o = 3 cos o

To find:-

• Cos o = ?

Solution:-

Therefore,Sin o = 3/4 cos o

And cos o = 4/3 sin o

We know that

$\large\sf\red{tan{\theta = {\frac{Sin{\theta}{Cos{\theta}}}}}}$

$\sf \implies \: \frac{ \frac{3cos \theta}{4} }{cos \theta} \\ \\ \sf \implies \: \frac{3}{4}$

But

$\large\sf\green{tan{\theta={\frac{Perpendicular}{Base}}}}$

Let the Perpendicular and base = 3x and 4x respectively.

Therefore, we got

• Perpendicular = 3
• Base = 4

Using Pythagorean theorem.

$\large\sf\purple{H}^{2}$$\large\sf\purple{=B}^{2}+{H}^{2}$

$\sf \implies \: {4}^{2} + {3}^{2} \\ \\ \sf \implies \: 16 +9 \\ \\ \sf \implies \: 25$

We got, Hypotenuse = √25 = 5

Now,

Sin o = H/P

= 3/5

Cos o = 4/3 × 3/5 = 4/5