Graphs of trigonometric functions Flashcards
For an angle θ in a right angled triangle, what is sin(θ) equal to?
opposite/hypotenuse
For an angle θ in a right angled triangle, what is cos(θ) equal to?
adjacent/hypotenuse
For an angle θ in a right angled triangle, what is tan(θ) equal to?
opposite/adjacent
What convention is used when referring to angles in an x–y plane?
It goes anticlockwise, measured from the positive x axis
Which out of sin(θ), cos(θ) and tan(θ) are positive in the first quadrant?
All of them
Which out of sin(θ), cos(θ) and tan(θ) are positive in the second quadrant?
sin(θ)
Which out of sin(θ), cos(θ) and tan(θ) are positive in the third quadrant?
tan(θ)
Which out of sin(θ), cos(θ) and tan(θ) are positive in the fourth quadrant?
cos(θ)
What is sin(180°-θ) equal to?
sin(θ)
What is sin(180°+θ) equal to?
-sin(θ)
What is sin(360°-θ) equal to?
-sin(θ)
What is cos(180°-θ) equal to?
-cos(θ)
What is cos(180°+θ) equal to?
-cos(θ)
What is cos(360°-θ) equal to?
cos(θ)
What is tan(180°-θ) equal to?
-tan(θ)
What is tan(180°+θ) equal to?
tan(θ)
What is tan(360°-θ) equal to?
-tan(θ)
What is sin(0°)?
0
What is sin(30°)?
0.5
What is sin(45°)?
√(2)/2
What is sin(60°)?
√(3)/2
What is sin(90°)?
1
What is cos(0°)?
1
What is cos(30°)?
√(3)/2
What is cos(45°)?
√(2)/2
What is cos(60°)?
0.5
What is cos(90°)?
0
What is tan(0°)?
0
What is tan(30°)?
√(3)/3
What is tan(45°)?
1
What is tan(60°)?
√(3)
What is tan(90°)?
Undefined
What is sin(θ+360°) equal to?
sin(θ)
What is sin(θ-360°) equal to?
sin(θ)
What is sin(90°-θ)-sin(90°+θ) equal to?
0
What is cos(θ+360°) equal to?
cos(θ)
What is cos(θ-360°) equal to?
cos(θ)
What is cos(-θ)-cos(θ) equal to?
0
What is tan(θ+180°) equal to?
tan(θ)
What is tan(θ-180°) equal to?
tan(θ)
What does the graph of y=f(x+a) where a is a constant look like, compared to the graph of y=f(x)?
It has been horizontally translated by -a
What does the graph of y=f(x)+a where a is a constant look like, compared to the graph of y=f(x)?
It has been vertically translated by a
What does the graph of y=f(ax) where a is a constant look like, compared to the graph of y=f(x)?
It has been horizontally stretched by a scale factor of 1/a
What does the graph of y=af(x) where a is a constant look like, compared to the graph of y=f(x)?
It has been vertically stretched by a scale factor of a
What is sin(-θ) equal to?
-sin(θ)
What is cos(-θ) equal to?
cos(θ)
What is tan(-θ) equal to?
-tan(θ)
What is sin(90°-θ) equal to?
cos(θ)
What is cos(90°-θ) equal to?
sin(θ)
