GP3-­‐PAP Precalculus Selected Solutions from Section 7.2 on page 526 Solution Subtract tan! 𝜃 from both sides, 1 = sec ! 𝜃 − tan! 𝜃 sec ! 28! − tan! 28! = 1 Solution 1
sin 80!
=
= 1 sin 80! sin 80!
sin 80! csc 80! = sin 80!
sin 80! csc 80! = 1 Solution tan 50! −
sin 50!
= tan 50! − tan 50! = 0 cos 50!
sin 50!
tan 50 −
= 0 cos 50!
!
Solution cot 25! −
cot 25! −
cos 25!
= cot 25! − cot 25! = 0 sin 25!
cos 25!
= 0 sin 25!
Solution Tangent and cotangent are cofunctions and 12! and 78! are complementary angles, tan 12! = cot 78! tan 12! − cot 78! = 0 Solution Cosine and sine are cofunctions and 10! and 80! are complementary angles, cos 10! = sin 80! cos 10! sin 80!
=
= 1 sin 80! sin 80!
cos 10!
= 1 sin 80!
Solution Cosine and sine are cofunctions and 40! and 50! are complementary angles, cos 40! = sin 50! cos 40! sin 50!
=
= 1 sin 50! sin 50!
cos 40!
= 1 sin 50!
Solution 1 − cos ! 20! − cos ! 70! = 1 − cos ! 20! + cos ! 70! Cosine and sine are cofunctions and 20! and 70! are complementary angles,cos 20! = sin 70! 1 − cos ! 20! + cos ! 70! = 1 − sin! 70! + cos ! 70! = 1 − 1 = 0 1 − cos ! 20! − cos ! 70! = 0 Solution 1 + tan! 5! − csc ! 85! = sec ! 5! − csc ! 85! Secant and cosecant are cofunctions and 5! and 85! are complementary angles, sec 5! = csc 85! sec ! 5! − csc ! 85! = csc ! 85! − csc ! 85! = 0 1 + tan! 5! − csc ! 85! = 0 Solution Sine and cosine are cofunctions and 70! and 20! , cos 70! = sin 20! cos 70!
sin 20!
!
tan 20! −
=
tan
20
−
= tan 20! − tan 20! = 0 cos 20!
cos 20!
cos 70!
tan 20! −
= 0 cos 20!