Question

Given sin(−θ)=−1/6 and tanθ=−√35/35 What is the value of cosθ?

Answer 1

Answer:

$cos(\theta)=-\frac{\sqrt{35} }{6}$

Step-by-step explanation:

Recall the negative angle identity for the sine function:

$sin(- \theta)=-sin(\theta)$  

Then, we can find the value of  $sin(\theta)$:

$sin(\theta)=-sin(-\theta)\\sin(\theta) =-(-\frac{1}{6} )\\sin(\theta)= \frac{1}{6}$

Now recall the definition of the tangent function:

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

Therefore, now that we know the value of $sin(\theta)$, we can solve in this equation for $cos(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\-\frac{\sqrt{35} }{35} =\frac{1/6}{cos(\theta)} \\cos(\theta)=-\frac{\frac{1}{6} }{\frac{\sqrt{35} }{35} } \\cos(\theta)=-\frac{35}{6\,\sqrt{35} } \\cos(\theta)=-\frac{\sqrt{35} }{6}$