Question

How do i solve number 2The drawings are already drawn.

Answer 1

If Cos(θ)=12/13 it means that we can form a triangle with hypotenuse 13 and adjacent length 12. Using them to find the opposite length with the pythagorean theorem, we have:

`\begin{gathered} a^2+b^2=c^2 \\ (12)^2+b^2=13^2\text{ (Replacing the values)} \\ 144+b^2=169\text{ (Raising the numbers to the power of 2)} \\ b^2=25\text{ }(\text{Subtracting 144 from both sides of the equation)} \\ b=5\text{ (Taking the square root of both sides)} \\ \text{The opposite length is 5} \end{gathered}`

If the opposite length is 5 and the angle is in the fourth quadrant then sin(θ)=-5/13.

Given that sin(2θ)=2sin(θ)cos(θ), then sin(2θ)=2(-5/13)(12/13)= -120/169.

Given that cos(2θ)=cos^2(θ)-sin^2(θ), then cos(2θ)=(12/13)^2 - (-5/13)^2 =119/169

Answers:

cos(θ)=12/13

sin(θ)=-5/13

sin(2θ)=-120/169

cos(2θ)=119/169