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nasty-shy [4]
4 years ago
10

How is this worked out ? im confused.

Mathematics
1 answer:
Rudik [331]3 years ago
7 0

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}}

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