Q:

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

Accepted Solution

A:
Answer:[tex]\cos(\theta)=\pm \frac{24}{25}[/tex]Step-by-step explanation:I don't know where [tex]\theta[/tex] is so there is going to be two possibilities for cosine value, one being positive while the other is negative.A Pythagorean Identity is [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex].We are given [tex]\sin(\theta)=\frac{7}{25}[/tex].So we are going to input [tex]\frac{7}{25}[/tex] for the [tex]sin(\theta)[/tex]:[tex]\cos^2(\theta)+(\frac{7}{25})^2=1[/tex][tex]\cos^2(\theta)+\frac{49}{625}=1[/tex]Subtract 49/625 on both sides:[tex]\cos^2(\theta)=1-\frac{49}{625}[/tex]Find a common denominator: [tex]\cos^2(\theta)=\frac{625-49}{625}[/tex][tex]\cos^2(\theta)=\frac{576}{625}[/tex]Square root both sides:[tex]\cos(\theta)=\pm \sqrt{\frac{576}{625}}[/tex][tex]\cos(\theta)=\pm \frac{\sqrt{576}}{\sqrt{625}}[/tex][tex]\cos(\theta)=\pm \frac{24}{25}[/tex]