Question

A
Find tan a.
r
√5,-√7)
✓[?
Enter

Answer 1

tan α = -√35/5

Explanation:

tan α = y/x

tan α = -√7/√5

tan α = -√7/√5 × √5/√5

tan α = -√35/5

Answer 2

`tan(\alpha)=-(√(35))/(5)`

Explanation:

Tan can be defined as:
`(sin(\theta))/(cos(\theta))` as it simplifies to opposite/adjacent. If you know a bit about the unit circle, you'll know that the x-coordinate is going to be cos(theta) and the y-coordinate is going to be sin(theta). Since the sin(theta) is defined as opposite/hypotenuse, and the hypotenuse = 1, so sin(theta) is defined as the opposite side, which is the y-axis. Same thing goes for cos(theta), except the adjacent side is the x-axis.

Using this we can define tan

`sin(\alpha)=-√(7)\\cos(\alpha)=√(5)\\\\tan(\alpha)=-(√(7))/(√(5)) * (√(5))/(√(5))\\tan(\alpha)=-(√(7*5))/(5)\\tan(\alpha)=-(√(35))/(5)\\`