Question

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 functions for angle theta?

Answer 1

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

Explanation:

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

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,

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

$r=\sqrt{ \frac{2}{4}+\frac{2}{4}}$

$r=1$

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

$a=\frac{-\sqrt{2}} {2}$

$b=\frac{\sqrt{2}} {2}$

The formula for cosine,

$\cos \theta =\frac{a}{r}$

$\cos \theta =\frac{\frac{-\sqrt{2}} {2}}{1}}$

$\cos \theta =\frac{-\sqrt{2}} {2}}$

The formula for cotangent,

$\cot \theta =\frac{a}{b}$

$\cos \theta=\frac{\frac{-\sqrt{2}} {2}}{\frac{\sqrt{2}} {2}}$

$\cos \theta=-1$

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

Answer 2

Answer:a

Step-by-step explanation:

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