Q:

What is y = tan θ when θ = π?

Accepted Solution

A:
Answer:y = tan(π) = 0 ⇒ the third answerStep-by-step explanation:* Lets think how to solve the problem∵ y = tanФ ∵ tanФ = sinФ/cosФ∵ Ф = π* Find sinπ and cosπ by find where is the angle π located- The unit circle intersect x-axis at point (1 , 0) and (-1 , 0)- The unit circle intersect y-axis at point (0 , 1) and (0 , -1)∵ cosФ = x-coordinates of the points∵ sinФ = y-coordinates of the points- The positive part of x-axis has angle -2π , 0 , 2π- The negative part of x-axis has angle -π , π- The positive part of y-axis has angle -3π/2 , π/2- The negative part of y-axis has angle -π/2 , 3π/2∴ The angle of measure π lies on the -ve part of x-axis∴ cos(π) = -1 and sin(π) = 0* Lets substitute them in tanФ∴ tan(π) = sin(π)/cos(π) = 0/-1 = 0* y = tan(π) = 0