Question

If θ is a second-quadrant angle and cosθ = - 2/3, then tanθ=

a. -2 (sqrt 5)/5
b. - (sqrt 5)/2
c. - (sqrt 5)/3

Answer 1

In second Quadrant cos is negative

• cosØ=b/h=2/3

So

b=2 and h=3

Perpendicular

• p²=h²-b²
• p²=3²-2²
• p²=5
• p=√5

tanØ=-p/b =-√5/2

Answer 2

since in second quadrant cos θ is negative.

Cos θ=b/h=2/3

b=2

h=3

p=√(3²-2²)

p=√5

Now

Tan θ=p/b=√5/2

since in second quadrant tanθ is negative

so

Tanθ=-√5/2

b. - (sqrt 5)/2