Definitions
What is the definition of a right triangle?
A triangle with a 90 degree angle
Name the two special right triangles.
30-60-90 degree triangle and 45-45-90 degree triangle
What is the Unit Circle?
A circle with a center at the origin and a radius of 1.
What is the tangent identity?
Which of the trig functions are positive in the third quadrant?
Tangent and Cotangent.
Name a common mnemonic used to remember the first three trig functions?
SohCahToa
Name the first three trig functions and their formulas.
Sine, Cosine, and Tangent. Opposite over hypotenuse, adjacent over hypotenuse, and opposite over adjacent. Or y/1, x/1, and y/x.
What are the coordinates for a 60 degree central angle on the unit circle?
(1/2, square root 3/2)
What is the Pythagorean Identity?
cos^2t + sin^2t = 1
Find the reference angle of 130 degrees.
50 degrees
State the cofunction identity.
If any two angles are complementary, the sine of one is the cosine of the other, and vice versa.
Name the last three trig functions and their formulas.
Secant, Cosecant, and Cotangent. Hypotenuse over adjacent, hypotenuse over opposite, and adjacent over opposite. Or 1/x, 1/y, and x/y.
Name three of the five common angles on the unit circle.
0, 30, 45, 60, and 90 degrees
Name an alternate form of the Pythagorean Identity.
1 + cot^2t = csc^2t
Name the sine cofunction identity.
sin t = cos(pi/2 - t)
What formula does one use when converting from degrees to radians and how many radians equal 360 degrees?
pi/180 and 2pi
Given the triangle: hypotenuse = 17, opposite = 8, and adjacent = 15. Find all six trig functions of a.
sin = 8/17
cos = 15/17
tan = 8/15
sec 17/15
csc = 17/8
cot = 15/8
In the unit circle, which is the x coordinate and which is the y coordinate?
x coordinate = cos t
y coordinate = sin t
(cos t, sin t)
Simplify (tan t)(cos t)
sin t
Answer this problem: To find the height of a tree, a person walks to a point 30ft from the base of the tree. She measures an angle 57 degrees between a line of sight to the top of the tree and the ground. Find the height of the tree.
Answer: h = 46ft tall
What is the formula for area of a sector?
A = 1/2(theta)r^2
Find the exact value of the trigonometric functions of pi/3, using side lengths.
Sin pi/3 = square root 3/2
Cos pi/3 = 1/2
Tan pi/3 = square root 3
Sec pi/3 = 2
Csc pi/3 = 2square root 3/3
Cot pi/3 = square root 3/3
Name the five common angles on the unit circle in radians.
0, pi/6, pi/4, pi/3, and pi/2 radians
Name two of the fundamental trig identities, other than sin and cos.
tan t = sin t/cos t
sec t = 1/cos t
csc t = 1/sin t
cot t = cos t/sin t
Name the angular speed formula. Complete the problem: A point P on a circle rotates through 3pi/4 radians in 3 seconds. Give the angular speed of P.
w = theta/t and pi/4 rad/sec