Chapter 9 Section 1
What is the Pythagorean Identity and its definition?
sin^2 + cos^2 = 1. An equation involving a trigonometric function based on the properties of a right triangle.
State the sum identity for cosine.
cos(a+b) = cosa cosb - sina sinb
What is a double angle formula and what is the sine double angle formula?
a special case of the sum formulas, where 𝛼=𝛽. sin(2(theta)) = 2 sin theta cos theta
What is the cos to cos product to sum formula?
Cosa cosb = ½[cos(a-b) + cos(a+b)]
Solve the equation exactly: cos^2(theta) + 3cos(theta) - 1 = 0, 0<theta<2pi
1.26 or 5.02
Which two of the six even-odd identities are positive?
cos and sec
State the difference identity for sine.
sin(a-b) = sina cosb- cosa sinb
What is a reduction formula and is the tangent reduction formula?
They are formulas we can use to reduce the power of a given expression involving even powers of sine or cosine. tan^2theta = 1 - cos2theta/1 + cos2theta
What is one of the cos to cos sum to product formulas?
cosα−cosβ=−2sin(α+β/2)sin(α−β/2)
Solve exactly: 2sin^2(theta) + sin(theta) = 0, 0<theta<2pi
0, pi, 7pi/6, and 11pi/6
What are the sin and tan reciprocal identities?
sinx = 1/cscx and tanx = 1/cotx
State the secant cofunction identity.
sec(pi/2 - x)
What is a half angle formula and what is the cosine half angle formula?
A formula that can be derived from the reduction formulas and we can use when we have an angle that is half the size of a special angle. cos(α/2)=±sqrt1+cosα/2
What is the sin to sin product to sum formula?
sina sinb = ½[cos(a-b) - cos(a+b)]
Solve the equation exactly using a double-angle formula: cos(2(theta)) = cos theta
-1/2, 1
State the definition of a quotient identity and name the two quotient identities.
It is an identity that defines relationships among certain trigonometric functions. Tanx = sinx/cosx and Cotx = cosx/sinx
State the difference identity for tangent.
tan(a-b) = (tan a- tan b)/1 + tan a tan b
Given that tan(theta) = -3/4 and theta is in quadrant 2, find the following:
sin(2(theta))
tan(2(theta))
sin(2(theta)) = -24/25
tan(2(theta)) = 7/25
Express the following product as a sum containing only sine or cosine and no products: sin(4theta)cos(2theta)
1/2[sin(6theta)+sin(2theta)]
Solve exactly: cos(2x) = 1/2 on [0, 2pi)
pi/6, 5pi/6, 7pi/6, and 11pi/6
Verify the identity: (sin^2(-theta)-cos^2(-theta))/sin(-theta)-cos(-theta) = cos(theta)-sin(theta)
cos(theta)-sin(theta)
Given sin a = 3/5, 0 < a < pi/2, cos B = -5/13, pi < b < 3pi/2, find
sin(a+b)
cos(a+b)
tan(a+b)
sin(a+b) = -63/65
cos(a+b) = 16/65
tan(a+b) = -63/16
Given that tan a = 8/15 and a lies in quadrant 3, find the exact value of the following:
sin(a/2)
cos(a/2)
sin(a/2) = 4sqrt17/17
cos(a/2) = -sqrt17/17
Evaluate cos(15) - cos(75)
sqrt2/2
Solve the equation exactly using an identity: 3cos(theta) + 3 = 2sin^2(theta) 0<theta<2pi
2pi/3, 4pi/3, and pi