Chapter 6 Trigonometric Functions (Year 2) Flashcards
What is secx equivalent to?
Secx = 1/cosx
What is cosecx equivalent to?
Cosecx = 1/sinx
What is cotx equivalent to?
Cotx = 1/tanx and cosx/sinx
What are the properties of the graph of y = secx?
- symmetry in the y-axis
- has a period of 360 degrees
- vertical asymptotes at all of the values of x for which cosx = 0
What is the domain of y = secx?
x /= any odd multiple of 90 degrees/pi/2 radians
What is the range of y=secx?
y <= -1 or y>= 1
What are the properties of the graph of y = cosecx?
- period of 360 degrees
- vertical asymptotes at all of the values of x for which sinx = 0
What is the domain of y = cosecx?
x /= any multiple of 180 degrees/pi radians
What is the range of y = cosecx?
y <= -1 or y >= 1
What are the properties of the graph of y = cotx?
- period of 180 degrees
- vertical asymptotes at all of the values of x for which tanx = 0
What is the domain of y = cotx?
x /= any multiple of 180 degrees/pi radians
What is the range of y = cotx?
All real values
When does secx = k have no solutions?
When -1 < k < 1
When does cosecx = k have no solutions?
When -1 < k < 1
What is sec^2x equivalent to?
1 + tan^2x
What is cosec^2x equivalent to?
1 + cot^2x
What is the inverse function of sinx called?
Arcsinx
What is the domain and range of arcsinx?
Domain: -1 <= x <= 1
Range: -90 degrees <= arcsinx <= 90 degrees
What is the inverse function of cosx called?
Arccosx
What is the domain and range of arccosx?
Domain: -1 <= x <= 1
Range: 0 <= arccos <= 180 degrees
What is the inverse function of tanx called?
Arctanx
What is the domain and range of arctanx?
Domain: any values of x
Range: -90 degrees <= arctan <= 90 degrees
