MATH SOLVE

3 months ago

Q:
# Use 90°<θ<180° and sin θ=24/25 to answer the following questions. What is cos θ?

Accepted Solution

A:

Answer:-7/25Step-by-step explanation:[tex]\theta[/tex] is in quadrant two given that [tex]\theta[/tex] is between 90 degrees and 180 degrees.This means cosine value there is negative and sine value is positive.Let's use the Pythagorean Identity: [tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex].[tex](\frac{24}{25})^2+\cos^2(\theta)=1[/tex][tex]\frac{576}{625}+\cos^2(\theta)=1[/tex]Subtract 576/625 on both sides:[tex]\cos^2(\theta)=1-\frac{576}{625}[/tex][tex]\cos^2(\theta)=\frac{625-576}{625}[/tex][tex]\cos^2(\theta)=\frac{49}{625}[/tex]Take the square root of both sides:[tex]\cos(\theta)=\pm \frac{7}{25}[/tex]So recall that the cosine value here is negative due to the quadrant we are in.[tex]\cos(\theta)=-\frac{7}{25}[/tex]Check:[tex](\frac{24}{25})^2+(-\frac{7}{25})^2[/tex][tex]\frac{576+49}{625}[/tex][tex]\frac{625}{625}[/tex][tex]1[/tex]So we got the desired result since the right hand side of our Pythagorean Identity is 1.