Question

The point (Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, StartFraction StartRoot 2 EndRoot Over 2 EndFraction) 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? cosine theta = Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = negative 1 cosine theta = StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = 1 cosine theta = StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = negative one-half cosine theta = Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = one-half

Answer 1

The cosine function is -√2/2 and the cotangent function is 1.

Step-by-step explanation:

The point (-√2/2, √2/2) on the unit circle represents the terminal ray of angle θ. The cosine function is equal to the x-coordinate of this point, which is -√2/2. Therefore, cosine θ = -√2/2.

The cotangent function is equal to the reciprocal of the tangent function. The tangent function is equal to the y-coordinate divided by the x-coordinate of the point on the unit circle. In this case, the y-coordinate is √2/2 and the x-coordinate is -√2/2. So, the tangent function is -1. Therefore, the cotangent function is the reciprocal of -1, which is 1.

Answer 2

`\cot(x) = - 1 \: and \: \cos(x) = - ( √(2) )/(2)`

Step-by-step explanation:

The given point is :

`( - ( √(2) )/(2), ( √(2) )/(2))`

This point is in the second quadrant.

This means:

`\cos(x) = - ( √(2) )/(2), \sin(x) = ( √(2) )/(2))`

Cotangent is cosine/sine

`\cot(x)=( ( √(2) )/(2) )/( - ( √(2) )/(2) ) = - 1`