Question

If cos A=9/41,find other trigonometric ratios of angle A

Answer 1

here is ur answer,
sinA=40/41
tanA=40/9

Answer 2

Sin A = 40/41 ,

Cos A = 9/41,

Tan A = 40/9,

Cosec A = 41 /40 ,

Sec A = 41/9 ,

Cot A = 9/40.

Given :

cos A = 9/41

To find :

Other trigonometric ratios of angle A

Solution :

The triangle drawn has right angle at B

Hence, Cos A = AB/AC = 9/41

Let AB = 9k and AC = 41k where k is +ve.

Applying Pythagoras theorem,

AC^2 = AB^2 + BC^2

=> BC^2 = AC^2 - AB^2

=> BC^2 = (41k)^2 - (9k)^2 - (81k)^2 = 1600k^2

BC = √1600k^2

= 40k

Sin A = BC/AC = 40k/41k = 40/41

Cos A = 9/41 (given)

Tan A = Sin A/Cos A = 40/41 ÷ 9/41

= 40/9

Cosec A = 1/sin A = 41 /40

Sec A = 1 / cos A = 41/9

Cot A = 1/Tan A = 9/40

Hence, Sin A = 40/41 , Cos A = 9/41, Tan A = 40/9, Cosec A = 41 /40 , Sec A = 41/9 , Cot A = 9/40.

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