Question

Given that sin0= 3/5 and 0 lies in Quadrant 1, what does cos0 equal?

Answer 1

cosine (θ) = 4/5

1) Given that the sin(θ) is in Quadrant I , and θ lies in this quadrant too

Let's remind the signal fo that:

2) Let's use the Pythagorean Identity to find the value of the cosine (θ):

`\begin{gathered} \sin ^2(\theta)\text{ +}\cos ^2(\theta)\text{ =1} \\ ((3)/(5))^2+\cos ^2(\theta)\text{ =1} \\ \cos (\theta)\text{ =}\sqrt[]{1-(9)/(25)} \\ \cos \text{ (}\theta)\text{ =}\sqrt[]{(25)/(25)-(9)/(25)} \\ \cos \text{ (}\theta)\text{ =}\sqrt[]{(16)/(25)} \\ \cos \text{ (}\theta)=(4)/(5) \end{gathered}`

3) As the value of the sine and the cosine in Quadrant I is positive then we can state the cosine (θ) = 4/5