Respuesta :
The values of cosine Ф and cotangent Ф are [tex]\frac{-\sqrt{2} }{2}[/tex] and -1
Step-by-step explanation:
When a terminal side of an angle intersect the unit circle at
point (x , y), then:
- The x-coordinate is equal to cosine the angle between the positive part of x-axis and the terminal side
- The y-coordinate is equal to sine the angle between the positive part of x-axis and the terminal side
- If x and y coordinates are positive, then the angle lies in the 1st quadrant
- If x-coordinate is negative and y-coordinate is positive, then the angle lies in the 2nd quadrant
- If x and y coordinates are negative, then the angle lies in the 3rd quadrant
- If x-coordinate is positive and y-coordinate is negative, then the angle lies in the 4th quadrant
∵ The terminal ray of angle Ф intersects the unit circle at point [tex](\frac{-\sqrt{2} }{2},\frac{\sqrt{2} }{2})[/tex]
- According to the 1st and 2nd notes above
∴ cosФ = x-coordinate of the point
∴ sinФ = y-coordinate of the point
∵ The x-coordinate of the point is negative
∵ They-coordinate of the point is positive
- According the the 4th note above
∴ Angle Ф lies in the 2nd quadrant
∵ x-coordinate = [tex]\frac{-\sqrt{2} }{2}[/tex]
∴ cosФ = [tex]\frac{-\sqrt{2} }{2}[/tex]
∵ y-coordinate = [tex]\frac{\sqrt{2} }{2}[/tex]
∴ sinФ = [tex]\frac{\sqrt{2} }{2}[/tex]
- cotФ is the reciprocal of tanФ
∵ tanФ = sinФ ÷ cosФ
∴ cotФ = cosФ ÷ sinФ
∴ cotФ = [tex]\frac{-\sqrt{2} }{2}[/tex] ÷ [tex]\frac{\sqrt{2} }{2}[/tex]
∴ cotФ = -1
The values of cosine Ф and cotangent Ф are [tex]\frac{-\sqrt{2} }{2}[/tex] and -1
Learn more:
You can learn more about the trigonometry function in brainly.com/question/4924817
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