Question

Angle θ has a terminal side located in Quadrant III of the coordinate plane and cos(θ)=−45.What is tan(θ)?

Answer 1

Given:

`cos\theta=-(4)/(5)\text{ and }\theta\text{ is in Quadrant III.}`

Required:

`We\text{ need to find tan}\theta.`

Step-by-step explanation:

Use the Pythagorean theorem to find the value of a.

`5^2=a^2+(-4)^2`
`25=a^2+16`
`25-16=a^2+16-16`
`9=a^2`

Take square root on both sides.

`√(9)=√(a^2)`
`\pm3=a`

Here a is negative since the angle is in Quadrant III.

`a=-3`

Consider the tangent.

`tan\theta=(a)/(-4)`

Substitute a =-3 in the equation.

`tan\theta=(-3)/(-4)`
`tan\theta=(3)/(4)`

Final answer:

`tan\theta=(3)/(4)`