Problem of the Day
Are the following equations true? If they are, show how.
1.
2.
3.
Problem of the Day
Verify the identity.
Problem of the Day
Use trig identities to find the missing trig values(Show work)
Find csc given cot = 3/4
Problem of the Day
Verify the trig identity
1. sin sec = tan
2. (sec2 ­ 1) cot2 = 1
Problem of the Day
Use trig identities to find, if is in Quadrant II.
Problem of the Day
Use trig identities to find the missing trig values. Find cos given sin = 4/7 and is in Quadrant II.
Problem of the Day
Verify the Identity
tany cosy + siny = 2siny
7­1 Basic Identities and Their Use
sin = 2/3 Find cos and tan tan = 4/5 Find sec
Use identities to find the trig functions.
1. find cscϴ
2. find sinϴ
3. find sinβ
Re­writing Identities
sin2x + cos2x = 1
tan2x + 1 = sec2x
1 + cot2x = csc2x
Verify the identity
sin cot = cos
(1­sin2 ) tan = cos sin Factoring
sin2B ­ sinB ­ 6 Verify the Identity
Distributing to Verify
(cscZ ­ cotZ)(cscZ + cotZ) + 1 = 2
(sinA + 1)(sinA ­ 1) = ­cos2A
Adding Expressions to Verify
Practice Problems
Verify the trig identity
1.(sinX + cosX)2 = 1 + 2sinXcosX
2. Practice Problems
Verify the trig identity
1 ­ cotYsinYcosY = sin2Y
Practice Problems
Verify the Trig Identity
1. cotYsecYsinY = 1
2. tanB + 1 = secB(sinB + cosB)
3. 4. = cscx + 2cosx Practice Problems
Verify the Trig Identity
1. (1 ­ cos2 )/cos2 = tan2
2. 1 ­ sinxcotxcosx = sin2x
3. Practice Problems
Verify the Trig Identity
Using Identities
­when given a numerical value, USE IDENTITIES
­when verifying an identity, start with the more complicated side of the equal sign
­start by seeing if basic algebra would be appropriate(factoring, distributive property, etc)
­replace one function and then the other if necessary
Using Identities(contd)
­simplify until the identity is verified
­be careful to only simplify to a reasonable point
(ie. Mr. Stalter is mean but would he really have you verify an identity that took you half a page of notebook paper?????)
­see how complicated the sides are supposed to be and map out an idea of how long it may take and use that as a guide
Readings and Examples
pgs 524­531
Homework: pg 531:1­17, 31­33, 37­39
Group Exit Slip
Verify the identity. Everyone does the problem on a half sheet. I am picking one for the group's credit.
Group Exit Slip