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Allisa [31]
3 years ago
7

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

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
6 0

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}

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