Right Triangles
What classifies a triangle as a right triangle?
90 degree angle
At what degrees/radians is cos(theta)=0? And sin (theta)=0?
Cosine: 90 degrees or pi/2, 270 degrees or 3pi/2
Sine: 180 degrees or pi, 360 degrees or 2pi
What is the radius of the unit circle?
1
What is tangent in terms of sine and cosine?
tan(x)=sin(x)/cos(x)
Write the equation for a cosine function with a stretch of 3, a horizontal shift to the right 2 and a vertical shift down 1.
y=3cos(x-2)-1
What famous theorem helps us find missing side lengths of right triangles?
Pythagorean Theorem
At what degrees and radians are cosine and sine the same value?
45 degrees or pi/4 and 225 degrees or 5pi/4
What trig functions represent the x and y values on the unit circle?
x=cos(theta), y=sin(theta)
At what degrees/radians is tan(theta) undefined?
when cos(theta)=0 so tan(theta) is undefined at 90 degrees or pi/2 and 270 degrees or 3pi/2
Are the graphs of sine and cosine continuous (a single unbroken curve)?
Yes
What are the two important types of right triangles named after their angles?
45-45-90 and 30-60-90
What are sine and cosine at 300 degrees?
(1/2, -sqrt(3)/2)
In which quadrants is cosine positive? Negative?
In which quadrants is sine positive? Negative?
Cosine: positive in quadrants I,IV and negative in quadrants II,III
Sine: positive in quadrants I,II and negative in quadrants III,IV
What is tan(45)?
tan(45)=1
What are the undefined values of tangent on a graph?
Asymptotes
Given a right triangle with a bottom angle of 42 degrees and bottom side 8 inches, find the hypotenuse using SOH CAH TOA.
cos(42)=8/c
c=8/cos(42)
c=10.77 inches
What are sine and cosine at 5pi/6?
(-sqrt(3)/2, 1/2)
What is the difference between degrees and radians?
Degrees measure angles, radians measure arc length
What is tan(2pi/3)?
tan(2pi/3)=-sqrt(3)
What are the maximum and minimum y-values of the equation y=cos(x)? What about y=sin(x)?
Both have maximum values of 1 and minimum values of -1.
What are the side length ratios for 45-45-90 and 30-60-90 triangles?
45-45-90: legs are 1 and hypotenuse is sqrt(2)
30-60-90: 1 and sqrt(3) accordingly and hypotenuse is 2
What is cos(450) and sin(5pi/2)?
and, 5pi/2-2pi=pi/2
so, 450 degrees=5pi/2
Then, cos(450)=0, sin(5pi/2)=1
What is the equation for the unit circle?
Plug in sin and cos to find an important trig identity.
x2+y2=1
Identity: cos2(theta)+sin2(theta)=1
What is tan(7pi/6)?
tan(7pi/6)= sqrt(3)/3
Name three points on the graph of the equation y=sin(x+pi/4).
Possible answers:
(-pi/4,0), (pi/4,1), (3pi/4,0), (5pi/4,-1), (7pi/4,0)