Question

If cosB=1/3 find the other five trigonometric ratios.

Answer 1

Cos B = 1/3 = B/H


B = 1 and H = 3.


By Pythagoras theroem,


( H )² = (B)² + (P)²


( 3)² = (1)² + (P)²




( P )² = 9 - 1


P² = 8


P = √8 = √2 × 2 × 2


P = 2√2.



Therefore,


Sin B = P/H = 2√2/3


Cos B = B/H = 1/3



Tan B = P/B = 2√2/1 = 2√2


Cosec B = H/P = 3/2√2



Sec B = H/B = 3


And,


Cot B = B/P = 1/2√2.

Answer 2

Step-by-step explanation:

Cos B = 1/3 = B/H

B = 1 and H = 3.

By Pythagoras theroem,

( H )² = (B)² + (P)²

( 3)² = (1)² + (P)²

( P )² = 9 - 1

P² = 8

P = √8 = √2 × 2 × 2

P = 2√2.

Sin B = P/H = 2√2/3

Cos B = B/H = 1/3

Tan B = P/B = 2√2/1 = 2√2

Cosec B = H/P = 3/2√2

Sec B = H/B = 3

Cot B = B/P = 1/2√2.

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