Question

If sin A = 8/17, find other trigonometric ratios of angle A.

Answer 1

Step-by-step explanation:

Answer = 8/15

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Answer 2

If sin A = 8/17, the other trigonometric ratios of angle A are cos A = $\frac{15}{17}$ , cosec A = $\frac{17}{8}$ , sec A = $\frac{17}{15}$ , tanA = $\frac{8}{15}$ and cot A = $\frac{15}{8}$.

Given : sin A = 8/17

To find: Other trigonometric ratios of angle A.

Solution:

Step1: Find base by using Pythagoras theorem, in the right ∆ ABC

$sin A = \frac{Perpendicular}{Hypotenuse} \\\\sin A =\frac{8}{17} =\frac{Perpendicular}{Hypotenuse}$

In the right ∆ ABC, by using Pythagoras theorem:

Perpendicular (BC) = 8 , Hypotenuse (AC) = 17 and Base (AB) = ?

AC² = AB² + BC²

17²  = AB² + 8²

289 = AB² + 64

AB² = 289 - 64

AB² = 225

AB = √225

AB = 15  

Base (AB) = 15

Step2: Find the other 5 trigonometric ratios:

$cos A = \frac{base}{Hypotenuse} \\\\cos A = \frac{15}{17}$

$cosec A = \frac{Hypotenuse}{Perpendicular} \\\\cosec A = \frac{17}{8}$

$sec A = \frac{Hypotenuse}{Base} \\\\sec A = \frac{17}{15}$

$tan A = \frac{Perpendicular}{Base} \\\\tanA = \frac{8}{15}$

$cot A = \frac{Base}{Perpendicular} \\\\cot A = \frac{15}{8}$

Hence, the other trigonometric ratios of angle A are cos A = $\frac{15}{17}$ , cosec A = $\frac{17}{8}$ , sec A = $\frac{17}{15}$ , tanA = $\frac{8}{15}$ and cot A = $\frac{15}{8}$.

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