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]
