Chapter 7
Name the two special right triangles.
30-60-90 degree triangle and 45-45-90 degree triangle
What is the arcsine?
another name for the inverse sine, x = sin^-1 x
What is one form of the Pythagorean Identity?
cos^2θ+sin^2θ=1
1+cot^2θ=csc^2θ
1+tan^2θ=sec^2θ
What is the law of sines?
sinα/a=sinβ/b=sinγ/c
a/sinα=b/sinβ=c/sinγ
What is the period of the sine trig graph?
2pi
Name three of the five common angles on the unit circle in degrees and radians.
0, 30, 45, 60, and 90 degrees
0, pi/6, pi/4, pi/3, and pi/2 radians
What is the formula for a shifted, compressed, and/or stretched cosecant function?
y = Acsc(Bx-C)+D
What is the secant reciprocal identity?
sec (theta) = 1/cos(theta)
What is the formula for area of oblique triangles?
Area=1/2bcsinα
=1/2acsinβ
=1/2absinγ
What is angular speed?
the angle through which a rotating object travels in a unit of time
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
What is a periodic function?
a function f(x) that satisfies f(x + P) = f(x) for a specific constant P and any value of x
What are the double angles formulas?
sin(2θ)=2sinθcosθ
cos(2θ)=cos^2θ−sin^2θ
=1−2sin^2θ
=2cos^2θ−1
tan(2θ)=2tanθ/1−tan^2θ
What does the law of cosines state?
it states that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the included angle
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
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
Determine the midline, amplitude, period, and phase shift of the function y = 3sin(2x) + 1.
A = 3
P = pi
D = 1
C/B = 0
What is the the sin plus sin sum to product formula?
2sin(α+β/2)cos(α−β/2)
Area = 29.4 square units
Name one of the quotient identities.
tanθ=sinθ/cosθ
cotθ=cosθ/sinθ
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
What is the phase shift?
the horizontal displacement of the basic sine or cosine function, the constant C/B
Use the double-angle formula for cosine to write cos(6x) in terms of cos(3x).
2cos^2(3x) - 1
Find the angle a for the given triangle if side a = 20, side b = 25, and side c = 18.
a = 52.4 degrees
If sinA = 12/13 and A is in the second quadrant and cosB = -8/17 and B is in the third quadrant, then find sinB.
sinB = -15/17