Question

Use the given information to find the exact value of a.sin 20, b.cos

Answer 1

Explanation:

`sin(2\theta)=2sin\theta~cos\theta\\\\cos(2\theta)=cos^2\theta-sin^2\theta\\\\cos\theta=(24)/(25)\\\\sin^2\theta+cos^2\theta=1~=>sin\theta=\pm√(1-cos^2\theta)\\\\we ~will~ use~ the ~minus~ sign~because~sin\theta~is~negative~in~IV~cuadrant\\sin\theta=-\sqrt{1-{((24)/(25))}^2}=-(7)/(25)`

Now we cal calculate the quantities requested

`sin(2\theta)=2sin\theta cos\theta=2(-(7)/(25))(24)/(25)=-(336)/(625)\\\\`

`cos(2\theta)=cos^2\theta-sin^2\theta=((24)/(25))^2-(-(7)/(25))^2=(527)/(625)`

`tan(2\theta)=(sin(2\theta))/(cos(2\theta))=(-(336)/(625))/((527)/(625))=-(336)/(527)`