5.1
5.2
5.3
5.4
Miscellaneous
100
Prove: cos0tan0 = sin0
cos0tan0 = cos0 x sin0/cos0, cos0tan0 = sin0
100
Write as a single trigonometric function: sin12xcos4x + cos12xsin4x =
sin16x
100
Let sinA = -3/5 with A in QIII, find sin2A
24/25
100
If cosA = 1/2 with A in QIV, find: sin(A/2)
1/2
100
List both of the ration identities.
tan0 = sin0/cos0 and cot0 = cos0/sin0
200
Prove: tan0/sec0 = sin0
sin0/cos0 x cos0 (reciprocal of sec0)= sin0, sin0cos0/cos0= sin0, (cos0 cancel out on top and bottom), sin0=sin0
200
Write as a single trigonometric function: sin10xcos2x + cos10xsin2x =
sin12x
200
Let tanx = 5/12 with x in QI, find sin2x
120/169
200
If cosA = 1/2 with A in QIV, find: csc(A/2)
2
200
Write cos4xcos5x - sin4xsin5x as a single trigonometric function.
cos9x
300
Prove: sec0cot0sin0 = 1
1/cos0 x cos0/sin0 x sin0 = 1, cos0sin0/cos0sin0=1, sin0 and cos0 both cancel out, 1=1
300
Expand the following, let ( ' ) be the symbol for degrees: sin62'
cos30'sin32' - sin30'cos32'
300
Simplify the following, let ( ' ) be the symbol for degrees: 2sin15'cos15'
sin30' = 1/2
300
If sinA = 4/5 with A in QII, and sinB = 3/5 with B in QI, find: sec2A
-25/7
300
List all of the sum and difference formulas
sin(A+B) = sinAcosB + cosAsinB sin(A-B) = sinAcosB - cosAsinB cos(A+B) = cosAcosB - sinAsinB cos(A-B) = cosAcosB + sinAsinB tan (A+B) = (tanA+tanB)/(1-tanAtanB) tan (A-B) = (tanA-tanB)/(1+tanAtanB)
400
Prove: cot0 - 1=cos0(csc0 - sec0)
cot0 - 1=cos0(csc0 - sec0), cos0/sin0 - 1= cos0/sin0 - cos0/cos0, cos0/sin0 - 1= cos0/sin0 - 1
400
Write as a single trigonometric function, let ( ' ) be the symbol for degrees: cos15'cos75' - sin15'sin75'
cos90' which can be simplified to 0.
400
If tanx = -12/5 with x in QIV, then what does sin2x equal?
-120/169
400
If sinA = 4/5 with A in QII, and sinB = 3/5 with B in QI, find: cos2A
-7/25
400
Find tanA if tanB = 1/2 and tan(A + B) = 3
tanA = 1
500
Prove: tan0(cos0 + cot0) = sin0 + 1
tan0(cos0 + cot0) = sin0 + 1, sin0/cos0(cos0 + cos0/sin0) = sin0 + 1, Multiply out the left side then cancel everything out, sin0 + 1 = sin0 + 1
500
Write a formula for sin2x by writing sin2x as sin(x+x) and using the formula for the sine of a sum.
sin2x = 2sinxcosx
500
Let ( ' ) be the symbol for degrees and solve: 1 - 2sin^2 (65') = ?
cos130'
500
If sinA = 4/5 with A in QII, and sinB = 3/5 with B in QI, find: cos(A - B)
0
500
Let sinA = 4/5 with A in the second quadrant and sinB = -12/13 with B in the third quadrant. Then cos(A-B) =
-33/65
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