Question

The point (-√2/2,√2/2) is the point at which the terminal ray of angle theta intersects the unit circle. what are the cosine and cotangent functions for angle theta

Answer 1

Answer:

Step-by-step explanation:

For a unit circle with radius r, and centre at the origin , the parametric form is

x = cos t and y = sin t where t is the angle made by the line joining (x,y) to origin with positive x axis.

Here we have cost and sint have values as negative of each other

cost = -sint

Or tant = -1

Tan is negative in II and IV quadrant.

Since x is negative and y is positive we find that the point lies in the II quadrant.

Hence cotangent and cosine both will be negative

When tan t = -1, cot t = 1/ tant = -1

$Sec t = -\sqrt{1+tan^2t} =-\sqrt{2}$

This gives cosine value = $\frac{-1}{\sqrt{2} } =\frac{-\sqrt{2} }{2}$

Answer 2

since that is the terminal point, then

$\bf \left( \stackrel{\stackrel{x}{cosine}}{-\cfrac{\sqrt{2}}{2}}~~,~~\stackrel{\stackrel{y}{sine}}{\cfrac{\sqrt{2}}{2}} \right)\qquad \qquad cos(\theta )=-\cfrac{\sqrt{2}}{2} \\\\\\ cot(\theta )=\cfrac{\stackrel{cosine}{-\frac{\sqrt{2}}{2}}}{\stackrel{sine}{\frac{\sqrt{2}}{2}}}\implies -\cfrac{\sqrt{2}}{2}\cdot \cfrac{2}{\sqrt{2}}\implies -1$