Question

If sin theta =7/25, use the Pythagorean identity to find cos theta

Answer 1

Answer:

$\cos(\theta)=\pm \frac{24}{25}$

Step-by-step explanation:

I don't know where $\theta$ is so there is going to be two possibilities for cosine value, one being positive while the other is negative.

A Pythagorean Identity is $\cos^2(\theta)+\sin^2(\theta)=1$.

We are given $\sin(\theta)=\frac{7}{25}$.

So we are going to input $\frac{7}{25}$ for the $sin(\theta)$:

$\cos^2(\theta)+(\frac{7}{25})^2=1$

$\cos^2(\theta)+\frac{49}{625}=1$

Subtract 49/625 on both sides:

$\cos^2(\theta)=1-\frac{49}{625}$

Find a common denominator:

$\cos^2(\theta)=\frac{625-49}{625}$

$\cos^2(\theta)=\frac{576}{625}$

Square root both sides:

$\cos(\theta)=\pm \sqrt{\frac{576}{625}}$

$\cos(\theta)=\pm \frac{\sqrt{576}}{\sqrt{625}}$

$\cos(\theta)=\pm \frac{24}{25}$