The point (- square-root 2/2, square-root2/2 is the point at which the terminal ray of angle theta intersects the unit circle. What are the values for the cosine and cotangent f…

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asked Jun 16, 2019 36.6k views

2 Answers

Svenningsson · Answer 1 · 2019-06-22T19:02:57+0000

Answer: The value of cosine is
$\frac{-√(2)} {2}$ and the value of cotangent is -1.

Step-by-step explanation:

The given point is
$(\frac{-√(2)} {2}},\frac{√(2)} {2})$ .

Since the x coordinate is negative and y coordinate is positive so the point must be lies in second quadrant.

The distance of the point from the origin is,

$r=\sqrt{(\frac{-√(2)} {2}-0)^2+(\frac{√(2)} {2}-0)^2}$

$r=\sqrt{ (2)/(4)+(2)/(4)}$

r=1

The given point is in the form of (a,b). So we get,

$a=\frac{-√(2)} {2}$

$b=\frac{√(2)} {2}$

The formula for cosine,

$\cos \theta =(a)/(r)$

$\cos \theta =\frac{\frac{-√(2)} {2}}{1}}$

$\cos \theta =\frac{-√(2)} {2}}$

The formula for cotangent,

$\cot \theta =(a)/(b)$

$\cos \theta=\frac{\frac{-√(2)} {2}}{\frac{√(2)} {2}}$

$\cos \theta=-1$

Therefore, the value of cosine is
$\frac{-√(2)} {2}$ and the value of cotangent is -1.