Question

If 12 cot = 5, find all the trigonometric ratios.

Answer 1

Correct Question ;-

If 12cotϴ = 5 , find all the trigonometric ratios.

Solution:-

Given ,

12cotϴ = 5

→ cot ϴ = 5/12

→ b/p = 5/12 { see fig. }

Let ,

$\frac{b}{p} = \frac{5}{12} = x$

$\implies \: \frac{b}{5} = \frac{p}{12} = x$

$\implies \: \frac{b}{5} = x \: \: \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \frac{p}{12} = x$

$\implies \: \bold{b = 5x} \: \: \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \bold{p =12 x}$

According to Pythagoras theorem ,

» h² = p² + b²

→ h² = (12x)² + (5x)²

→ h² = 144x² + 25x²

→ h² = 169x²

→ h = √(169x²)

→ h = 13x

Now ,

• sinϴ = p/h = 12x/13x = 12/13
• cosϴ = b/h = 5x/13x = 5/13
• tanϴ = p/b = 12x/5x = 12/5
• cosecϴ = h/p = 13x/12x = 13/12
• secϴ = h/b = 13x/5x = 13/5