Question

Cos:sin=13:12 find the value of tantheta,cosec theta and costheta

Answer 1

let cos α=13k
sinα=12k
sin^ 2α+cos^2α=1
k^2(12^2+13^2)=1
k=1/√(144+169)
k=1/√313
cosα=13/√313
sinα=12/√313
tanα=12/13
cosecα=√313/12

Answer 2

Answer:

The values are

$\tan \theta=\frac{12}{13}$

$\cos \theta=0.7345$

$cosec \theta=1.475$

Step-by-step explanation:

Given that

$\cos \theta:\sin \theta=13:12$

$\text{we have to find the value of }\tan\theta, \cosec \theta and \cos \theta$

$\text{Let }\cos \theta=13x\text{ and }\sin \theta=12x$

$\text{As }\sin^2 \theta+\cos^2 \theta=1$

$(13x)^2+(12x)^2=1$

$169x^2+144x^2=1$

$313x^2=1$

$x^2=\frac{1}{313}$

$x=0.0565$

Hence,

$\sin \theta=12x=12\times 0.0565=0.678$

$\cos \theta=13x=13\times 0.0565=0.7345$

$\cos \theta:\sin \theta=13:12$

$\frac{\cos \theta}{\sin\theta}=\frac{13}{12}$

$\frac{\sin \theta}{\cos\theta}=\frac{12}{13}$

$\tan \theta=\frac{12}{13}$

$cosec \theta=\frac{1}{\sin \theta}=\frac{1}{0.678}=1.475$