Download sin sin ≠

Name:___________________________________ Date:________________Period:_______
Obj: To state and use the Pythagorean Identities
Advanced Algebra and Trigonometry / Section 5.2 (Day #8)
Do Now:
1) Given:
sin 2   cos 2   1
A) Rewrite the equation if   90
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B) Rewrite the equation if   30
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C) Rewrite the equation if  

4
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2) A) If sin 2   cos 2   1 , solve for sin 2 
B) If sin 2   cos 2   1 , solve for cos 2  .
The Pythagorean Identities:
Hypotenuse
Opposite
(opposite)2 + (adjacent)2 = (hypotenuse)2

Adjacent
Divide by h 2
Divide by a 2
o2  a 2  h2
o2  a 2  h2
sin 2   cos 2   1
1  tan 2   sec 2 
IMPORTANT!
sin 2   sin  2
(sin  )(sin  )  sin( ) 2
Divide by o 2
o2  a 2  h2
1  cot 2   csc 2 
Name:___________________________________ Date:________________Period:_______
Obj: To state and use the Pythagorean Identities
sin 2   cos 2   1
Examples:
1) sin 2 430 + cos 2 430 
2) tan 2

1 
7
3) cot 2 25  csc 2 25 
4) 1  sin 2 30 =
5) cos 2   1 
1  tan 2   sec 2 
1  cot 2   csc 2 
Name:___________________________________ Date:________________Period:_______
Obj: To state and use the Pythagorean Identities
sin 2   cos 2   1
1  tan 2   sec 2 
1  cot 2   csc 2 
6) tan 2 10  sec 2 10 
7) sec 2 10  tan 2 10 
And now for something a little different…
8) Given that sin  
3
and  is an acute angle, find the value of cos using a trigonometric identity.
5
9) Given that sin  
1
and  is an acute angle, find the value of cos using a trigonometric identity.
2
Name:___________________________________ Date:________________Period:_______
Obj: To state and use the Pythagorean Identities
sin 2   cos 2   1
1  tan 2   sec 2 
10) Given that tan  
2
find sec .
3
11) Given that cot  
3
7
12) Given that csc  
5
, find cot .
3
find csc .
1  cot 2   csc 2 