Transcript Trig identities and solutions Jeopardy

Jeopardy
Simplify Trig
expressions
Verify Trig
Identities
Find all
Solutions
Solutions with
multiple angles
Solutions
with factoring
Q $100
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Q $200
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Q $300
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Q $400
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Q $500
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Q $500
Q $500
Q $500
$100 Question from Simplify
Trig expressions
Cos(x)Sec(x)
$100 Answer from Simplify Trig
expressions
1
$200 Question from Simplify
Trig expressions
Cos2(x)
1 – cos(x)
$200 Answer from Simplify Trig
expressions
Cot2(x)
$300 Question from Simplify
Trig expressions
Tan(x) + 1
Sec(x)
$300 Answer from Simplify Trig
expressions
Sin(x) + Cos(x)
$400 Question from Simplify
Trig expressions
Cot(x)(Tan(x) + Cot(x))
$400 Answer from Simplify Trig
expressions
2
Csc (x)
$500 Question from Simplify
Trig expressions
Sin2(x) – Tan2(x)
2
2
Tan (x)Sin (x)
$500 Answer from Simplify Trig
expressions
-1
$100 Question from Verify Trig
Identities
Sin(x)Sec(x) = Tan(x)
$100 Answer from Verify Trig
Identities
Proofs will vary
Sin(x)
1
Cos(x)
Sin(x)
Cos(x)
Tan(x)
$200 Question from Verify Trig
Identities
Tan(x)Cot(x) =
Sec(x)
Cos(x)
$200 Answer from Verify Trig
Identities
Tan(x) 1/tan(x)
Sec(x)
1
Sec(x)
Cos(x)
$300 Question from Verify Trig
Identities
1 – Cos(x) = Csc(x) – Cot(x)
Sin(x)
$300 Answer from Verify Trig
Identities
1
Sin(x)
-
Cos(x)
Sin(x)
Csc(x) - Cot(x)
$400 Question from Verify Trig
Identities
2
2
Sec (x)Csc (x)
=
2
Sec (x)
–
2
Csc (x)
$400 Answer from Verify Trig
Identities
(Tan2(x) + 1)Csc2(x)
Tan2(x)Csc2(x) + Csc2(x)
Sin2(x)
1
Cos2(x) Sin2(x)
1
Cos2(x)
+ Csc2(x)
+ Csc2(x)
Sec2(x) + Csc2(x)
$500 Question from Verify Trig
Identities
Cos(x)
1 – Sin(x)
+ 1 – Sin(x)
Cos(x)
= 2Sec(x)
$500 Answer from Verify Trig
Identities
Cos(x)(1 + Sin(x)) + Cos(x)(1 – Sin(x))
1 – sin2(x)
Cos2(x)
Cos(x) + Cos(x)Sin(x) + Cos(x) – Cos(x)Sin(x)
Cos2(x)
2Cos(x)
Cos2(x)
=
2
Cos(x)
= 2 Sec(x)
$100 Question from Find all
Solutions
Cos(x) = -1
2
$100 Answer from Find all
Solutions
X = 2 ∏ + 2∏n
3
X=4∏
3
+ 2 ∏n
$200 Question from Find all
Solutions
Sin(x) = √2
2
$200 Answer from Find all
Solutions
X = ∏ + 2 ∏n
4
X = 3 ∏ + 2 ∏n
4
$300 Question from Find all
Solutions
3Tan(x) = √3
$300 Answer from Find all
Solutions
X = ∏ + ∏n
6
$400 Question from Find all
Solutions
2Sin(x) + √3 = 0
$400 Answer from Find all
Solutions
X = 4 ∏ + 2 ∏n
3
X=5∏
3
+ 2 ∏n
$500 Question from Find all
Solutions
Sin(x) + 6 = -5Sin(x)
$500 Answer from Find all
Solutions
X = 3 ∏ + 2 ∏n
2
$100 Question from Solutions
with Multiple Angles [0 , 2∏)
Cos(2x) = -√2
2
$100 Answer from Solutions
with Multiple Angles [0 , 2∏)
X = 3 ∏ , 5 ∏ , 11 ∏ , 13 ∏
8
8
8
8
$200 Question from Solutions
with Multiple Angles [0 , 2∏)
Sin(3x) = √3
2
$200 Answer from Solutions
with Multiple Angles [0 , 2∏)
X = ∏ , 2 ∏ , 7 ∏ , 8 ∏ , 13 ∏ , 14 ∏
9
9
9
9
9
9
$300 Question from Solutions
with Multiple Angles [0 , 2∏)
Tan(4x) = -1
$300 Answer from Solutions
with Multiple Angles [0 , 2∏)
X = 3 ∏ , 7 ∏ , 11 ∏ , 15 ∏ ,
16
16
16
16
19 ∏ , 23 ∏ , 27 ∏ , 31 ∏
16
16
16
16
$400 Question from Solutions
with Multiple Angles [0 , 2∏)
Tan(x/2) = √3
$400 Answer from Solutions
with Multiple Angles [0 , 2∏)
X=2∏
3
$500 Question from Solutions
with Multiple Angles [0 , 2∏)
Cos(2X - ∏/4) = -√2
2
$500 Answer from Solutions
with Multiple Angles [0 , 2∏)
X=∏ , 3∏ , 3∏ , 7∏
2
4
2
4
$100 Question from Solutions
with factoring [0 , 2∏)
(Tan(x) + 1)(Sin(x) – 1) = 0
$100 Answer from Solutions
with factoring [0 , 2∏)
X=∏ , 3∏ , 7∏
2
4
4
$200 Question from Solutions
with factoring [0 , 2∏)
(2Cos(x) - √3)(2Sin(x) + 1) = 0
$200 Answer from Solutions
with factoring [0 , 2∏)
X = ∏ , 7 ∏ , 11 ∏
6
6
6
$300 Question from Solutions
with factoring [0 , 2∏)
2Sin2(x) + Sin(x) – 1 = 0
$300 Answer from Solutions
with factoring [0 , 2∏)
X=∏ , 5∏ , 3∏
6
6
2
$400 Question from Solutions
with factoring [0 , 2∏)
Sin2(x) + 2Sin(x) – 3 = 0
$400 Answer from Solutions
with factoring [0 , 2∏)
X=∏
2
$500 Question from Solutions
with factoring [0 , 2∏)
9Tan2(x) – 27 = 0
$500 Answer from Solutions
with factoring [0 , 2∏)
X = ∏ , 2∏ , 4∏ , 5∏
3
3
3
3