Blake is told that an angle has a cosine of −16√
and is in Quadrant III. Use the Pythagorean identity sin2(θ)+cos2(θ)=1
, the trigonometric identity tanθ=sinθcosθ
, and the quadrant to find the tangent. (1 point)
First, let's use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 to find the value of sine.
Since the angle is in Quadrant III, both sine and cosine will be negative.
Given that cos(θ) = -16√, we can square both sides to find sin(θ):
sin^2(θ) + (-16√)^2 = 1
sin^2(θ) + 256 = 1
sin^2(θ) = 1 - 256
sin^2(θ) = -255
Since sin(θ) can't be negative, we know that the equation has no real solutions in this case. Therefore, there is no tangent value we can find.