Question

--Given that sin(0)3/10and 0 is in Quadrant II, what is sin(20)?

Answer 1

Given the question in the image, the value for sin2Ф can be calculated using the following steps:

Step 1: Calculate the value for adjacent

`\begin{gathered} \sin \theta=(opp)/(hyp) \\ \text{opp}=3\sqrt[]{10} \\ \text{hyp}=10 \\ \text{adj}^2=hyp^2-opp^2 \\ \text{adj}=\sqrt[]{10^2-(3\sqrt[]{10)^2}} \\ \text{adj}=√(100-90) \\ adj=\sqrt[]{10} \end{gathered}`

Step 2: Calculate the value of sin2

`\begin{gathered} \sin 2\theta=2\sin \theta\cos \theta \\ \sin 2\theta=2(\frac{3\sqrt[]{10}}{10})(\frac{\sqrt[]{10}}{10}) \\ =2((3*10)/(100)) \\ 2*(30)/(100)=(60)/(100)=(2)/(5) \end{gathered}`

Hence, the result for the sin 2Ф is 2/5.