Question

How is this worked out ? im confused.

Answer 1

Answer:

From the given ratio for $tan\theta=\frac{4}{5}$ we found the values are

$sin\theta=4$  

$cos\theta=5$

$csc\theta=\frac{1}{4}$

$sec\theta=\frac{1}{5}$

$cot\theta=\frac{5}{4}}$

Step-by-step explanation:

Given the ratio for $tan\theta=\frac{4}{5}$

We have to find the rest of trignometric functions:

$tan\theta=\frac{4}{5}\hfill (1)$

$tan\theta$ can be written as

$tan\theta=\frac{sin\theta}{cos\theta}\hfill (2)$

Comparing equations (1) and (2) we get

$tan\theta=\frac{sin\theta}{cos\theta}=\frac{4}{5}$

$\frac{sin\theta}{cos\theta}=\frac{4}{5}$

Equating the coressponding numerator and denominator respectively

Therefore $sin\theta=4$ and $cos\theta=5$

We can find $csc\theta$

$csc\theta=\frac{1}{sin\theta}$

$=\frac{1}{4}$ (since $sin\theta=4$)

$csc\theta=\frac{1}{4}$

We can find $sec\theta$

$sec\theta=\frac{1}{cos\theta}$

$=\frac{1}{5}$ (since $cos\theta=5$)

$sec\theta=\frac{1}{5}$

To find $cot\theta$:

$cot\theta=\frac{1}{tan\theta}$

$=\frac{1}{\frac{4}{5}}$

$=1\times \frac{5}{4}$

$=\frac{5}{4}}$

$cot\theta=\frac{5}{4}}$