Question

20 POINTS. Given cos θ=4/5, find cot(θ).

Answer 1

`\displaystyle\\\cos\theta=(4)/(5)\\\\ \sin\theta=√(1-\cos^2\theta)=\sqrt{1-\left((4)/(5)\right)^2} =\sqrt{1-(16)/(25)} =\sqrt{(9)/(25)} =(3)/(5)~~\text{(If } \theta \in \text{quadrant 1)}}\\\\\\ \cot(\theta)=(\cos\theta)/(\sin\theta)=(~~(4)/(5)~~)/((3)/(5))=(4)/(5)*(5)/(3)=(4)/(3)\\\\\\\boxed{\cot(\theta)=(4)/(3)}`

.