Definitions
This is the definition of a right triangle.
What is triangle with a 90 degree angle?
These are the two special right triangles (think about angle measurements on the triangles we use within the unit circle).
What are 30-60-90 degree triangles and 45-45-90 degree triangles?
This is the definition of the Unit Circle.
What is a circle with a center at the origin and a radius of 1?
The tangent identity, which uses sine and cosine to calculate the tangent at a given point.
What is tan t = sin t/cos t?
These trig functions are positive in the third quadrant.
What are Tangent and Cotangent?
This is a common mnemonic used to remember the first three trig functions.
What is SohCahToa?
These the first three trig ratios and their formulas.
What are Sine, Cosine, and Tangent? Opposite over hypotenuse, adjacent over hypotenuse, and opposite over adjacent.
These are the coordinates for a 60 degree angle on the unit circle.
What is (1/2, square root 3/2)?
This is the Pythagorean Identity, which uses trigonometric ratios and the Pythagorean Theorem.
What is cos^2t + sin^2t = 1?
This is the reference angle of 130 degrees.
What is 50 degrees?
This trigonometric ratio represents the ratio between the side opposite from an angle divided by the side adjacent to an angle.
What is tangent?
These are the three reciprocal trig functions and their formulas.
What are Secant, Cosecant, and Cotangent? Hypotenuse over adjacent, hypotenuse over opposite, and adjacent over opposite.
Here are three of the five first-quadrant angles on the unit circle in degrees.
0, 30, 45, 60, and 90 degrees
These are two trigonometric ratios that are complementary.
What is sine and cosine?
What is secant and cosecant?
This is the sine cofunction identity.
What is sin t = cos(pi/2 - t)?
This is the formula one uses when converting from degrees to radians and how many radians equal 360 degrees.
What are pi/180 and 2pi?
Given the triangle: hypotenuse = 17, opposite = 8, and adjacent = 15, these are the sine, cosine, and tangent of a.
sin = 8/17
cos = 15/17
tan = 8/15
In the unit circle, we can represent x and y coordinates with trig functions by assigning x to ____ and y to ______.
What are?
x coordinate = cos t
y coordinate = sin t
(cos t, sin t)?
This is the simplified form of (tan t)(cos t).
What is sin t?
This is how to use the difference of cosines identity to prove the cosine co-function identity (cos(pi/2-t)=sin(t)).
What is substituting pi/2 and t into the difference of cosines formula, then simplifying until you get sin(t)?
sin(x+y)/cos(x+y)
(sinx*cosy+cosx*siny)/(cos*cosy-sinx*siny)
Divide everything by (cosx*cosy) and simplify.
These are the exact value of the trigonometric functions of pi/3.
What are:
Sin pi/3 = square root 3/2
Cos pi/3 = 1/2
Tan pi/3 = square root 3?
These are the five first-quadrant angles on the unit circle in radians.
What are 0, pi/6, pi/4, pi/3, and pi/2 radians?
This is the method you would use to use the Pythagorean Identity to show tan^2x+1=sec^2x.
Put the left side in terms of sine and cosine and simplify until you obtain the function on the right side.
This/these value(s) of x satisfy/satisfies the equation cos(x)=sin(x) on [0,2pi].
What is x=pi/4, 5pi/4