Answer:
[tex]\textsf{1)}\quad \cos \pi = -1[/tex]
[tex]\textsf{2)}\quad \tan\left(\dfrac{\pi}{2}\right)=\textsf{und\:\!efined}[/tex]
Step-by-step explanation:
A quadrantal angle is an angle in standard position in the Cartesian coordinate system whose terminal side coincides with one of the axes (x-axis or y-axis).
The unit circle is a circle centered at the origin (0, 0) with a radius of 1 unit. The x-coordinate of each point on the unit circle represents the cosine of the associated angle, and the y-coordinate represents the sine of the same angle. Angles are measured counterclockwise from the positive x-axis.
Question 1
When the angle is π, the terminal side aligns with the negative x-axis and the corresponding point on the unit circle is (-1, 0). Since the x-coordinate of the point represents the cosine of the angle, the cosine of π is equal to -1, so:
[tex]\Large\boxed{\boxed{\cos \pi = -1}}[/tex]
Question 2
When the angle is π/2, the terminal side aligns with the positive y-axis and the corresponding point on the unit circle is (0, 1). Consequently, cos(π/2) = 0 and sin(π/2) = 1.
Since the tangent of an angle is the ratio of the sine to the cosine of the angle, then:
[tex]\tan \left(\dfrac{\pi}{2}\right)=\dfrac{\sin\left(\dfrac{\pi}{2}\right)}{\cos\left(\dfrac{\pi}{2}\right)}=\dfrac{1}{0}=\textsf{und\:\!efined}[/tex]
When a number is divided by zero, it is undefined. Therefore:
[tex]\Large\boxed{\boxed{\tan \left(\dfrac{\pi}{2}\right)=\textsf{und\:\!efined}}}[/tex]
