Prove the following identities.tan 2' + cot 2' = 2 csc x

If 00 < A < 90, then AI2 terminates in which quadrant?

If 90 < A < 1800 , then AI2 terminates in which quadrant?

If 1800 < A < 2700 , then AI2 terminates in which quadrant?

If 270 < A < 3600 , then AI2 terminates in which quadrant?

If 1800 < A < 270, then is sin (AI2) positive or negative?

If 270 < A < 360, then is cos (AI2) positive or negative?

True or false: Ifsin A is positive, then sin (AI2) is positive as well.

True or false: If cos A is negative, then cos (AI2) is negative as well.

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360. If cos A = +with A in QIV, find sm 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360. If cos A = +with A in QIV, find cos 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360. If cos A = +with A in QIV, find csc 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360. If cos A = +with A in QIV, find sec 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.Ifsin A = -% with A in QIII, find cos 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.Ifsin A = -% with A in QIII, find sm 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.Ifsin A = -% with A in QIII, find sec-

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.Ifsin A = -% with A in QIII, find csc 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360. If sin B = -t with B in QIII, find sm 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360. If sin B = -t with B in QIII, find csc 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360. If sin B = -t with B in QIII, find cos 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360. If sin B = -t with B in QIII, find sec 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360. If sin B = -t with B in QIII, find tan

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360. If sin B = -t with B in QIII, find cot 2"

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find sin

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find cos 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find cos 2A

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find sin 2A

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find sec 2A

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find csc2A

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find cos

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find sm 2

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find sin (A + B)

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find cos (A + B)

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find cos (A - B)

Note For the following problems, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270 < A < 360.If sin A 1with A in QII, and sin B = ~ with B in QI, find sin (A B)

Graph each of the following from x = 0 to x = 41T. Y 4 sm~ "2

Graph each of the following from x = 0 to x = 41T.y = 6 cos "2

Graph each of the following from x = 0 to x = 41T.y - 2 cos 2

Graph each of the following from x = 0 to x = 41T.y = 2 sm2 2

Use half-angle formulas to find exact values for each of the following: cos 15

Use half-angle formulas to find exact values for each of the following: tan 15

Use half-angle formulas to find exact values for each of the following: sin 75

Use half-angle formulas to find exact values for each of the following: cos 75

Use half-angle formulas to find exact values for each of the following: cos 105

Use half-angle formulas to find exact values for each of the following: sin 105

Prove the following identities.sin2 9 csc 9 - cot () 2 csc ()

Prove the following identities.2 cos 2 sin2 9 ~cos()

Prove the following identities.sec2 =2 sec A sec A + 1

Prove the following identities.csc 2 2 sec A secA 2 sec A + 1 1

Prove the following identities.tan 2 = csc B cot B

Prove the following identities.tan 2 = sec B csc B + csc B

Prove the following identities.tan 2' + cot 2' = 2 csc x

Prove the following identities.tan 2' cot 2' = - 2 cot x

Prove the following identities.cos 2' 2 tan ()

Prove the following identities.2 sm 2' - 1 + cos ()

Prove the following identities.cos4 () +--+--

Prove the following identities.4 sin4 () = 1 - 2 cos 2() + cos2 29

The following problems review material we covered in Section 4.7. Reviewing these problems will help you with the next section. Evaluate without using a calculator or tables.sin (arcSin ~)

The following problems review material we covered in Section 4.7. Reviewing these problems will help you with the next section. Evaluate without using a calculator or tables.cos ( arcsin f)

The following problems review material we covered in Section 4.7. Reviewing these problems will help you with the next section. Evaluate without using a calculator or tables.cos (arctan 2)

The following problems review material we covered in Section 4.7. Reviewing these problems will help you with the next section. Evaluate without using a calculator or tables.sin (arctan 2)

Write an equivalent expression that involves x only. sin (tan-l x)

Write an equivalent expression that involves x only.cos (tan I x)

Write an equivalent expression that involves x only.tan (sin-1 x)

Write an equivalent expression that involves x only.tan (COS-I x)

Write an equivalent expression that involves x only.Graph y sin-I x.

Write an equivalent expression that involves x only.Graph y cos-1 x.

Navigation As we have seen in previous chapters, the great circle distance (in radians) between two points PI(LTI , LN1) and P2(LT2, LN2), whose coordinates are given as latitudes and longitudes, is calculated using the formula d COS-I (sin (LTI) sin (LT2) + cos (LT1) cos (LT2) cos (LNI - LN2 An alternate formula that can be used is ( .. LT} LT2 LN! LN2 d 1.;n-' Y,;n'( 2 ) + co, (LT,) 00' (LT,) sill' ( 2 )) Prove that by setting these two expressions equal to one another, the result is an identity.