Question

Given that sin(0)2/13and 0 is in Quadrant IV, what is cos(20)?13,

Answer 1

1) Let's use a trigonometric identity for this question:

`\begin{gathered} \cos (2\theta)=1-2\sin ^2(\theta) \\ \cos (2\theta)=1-2\cdot(\frac{-2\sqrt[]{13}}{13})^2 \end{gathered}`

Notice that for that double angle identity, we need to pick the one that relates the value of the sin(theta):

`\begin{gathered} \cos (2\theta)=1-2\cdot(\frac{-2\sqrt[]{13}}{13})^2 \\ \cos (2\theta)=1-2((52)/(169)) \\ \cos (2\theta)=1-2((4)/(13)) \\ \cos (2\theta)=1-(8)/(13)=(5)/(13) \end{gathered}`

2) In Quadrant IV the sign of the cosine function is :