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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 ______________________________ B) Rewrite the equation if 30 ______________________________ C) Rewrite the equation if 4 ______________________________ 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