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Name ______________________________ Date______________

WORKSHEET - THE BASIC 8 TRIG IDENTITIES

Simplify each expression to a single trig function or number.

1. sec θ sin θ 2. cos θ tan θ 3. tan2 θ – sec2 θ 4. 1 – cos2

θ 5. )cos1)(cos1( θ+θ− 6. )1x)(sec1x(sec +−

7. Atan

1

Asin

1

22− 8.

θ

θ−

2

2

tan

sin1

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9. θ

−

θ22 cot

1

cos

1 10. )cos(seccos θ−θθ

11. )1A(secAcos 22− 12. )x)(cosxsec1)(xcos1( +−

13. xcos1

xcosxsin

2−

14. 11sec

tan2

++θ

θ

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15. List the Basic 8 Identities.

Reciprocal Ratio Pythagorean

_______________ ________________

_______________ ________________

_______________

_______________ _______________

________________

REVIEW.

16. Find the following for an angle in standard position with measure 675°.

a) The quadrant in which the angle is located. ___________

b) The coterminal angle that is between 0° and 360°. _____________

c) The reference angle. ______________

17. Find the following for an angle in standard position with measure 7

10π−

a) The quadrant in which the angle is located. ___________

b) The coterminal angle that is between 0 and 2π. _____________

c) The reference angle. ______________

18. If cot θ= 7 and π<θ<π 2 , sketch the angle θ and find the value of the other five trig functions.

sin θ = ______ csc θ = ______ cos θ = ______ sec θ = ______ tan θ = ______

ANSWERS: 1. tanθ 2. sinθ 3. -1 4. sin2θ 5. sin

2θ 6. tan

2θ 7. 1 8. sin

2θ 9. 1 10. sin

2θ 11. sin

2A

12. sin2x 13. cotx 14. secθ 15. see notes 16. a) Q4 b) 315° c) 45° 17. a) Q2 b)

7

4π c)

7

3π

18. sinθ = 10

2−, cosθ =

10

27−, tanθ =

7

1, cscθ = -5 2 , secθ =

7

25−