ADDITION AND SUBTRACTION FORMULAS
ADDITION AND SUBTRACTION FORMULAS
sin [pic] = sin[pic]cos [pic] + cos [pic]sin[pic]
sin [pic] = sin [pic]cos[pic] - cos[pic]sin[pic]
cos [pic] = cos[pic]cos[pic] - sin[pic] sin[pic]
cos [pic] = cos[pic]cos[pic] + sin[pic]sin[pic]
tan [pic] = [pic]
tan [pic] = [pic]
COMBINATIONS
15[pic] = 345[pic] =
255[pic] = 75[pic] =
EXAMPLES
Evaluate each expression
1) sin 75[pic]
2) cos 345[pic]
3) tan 165[pic]
Simplify the following:
4) cos (270[pic] - x)
5) sin ( x + [pic]) =
6) cos ( [pic] )
Find each of the following numbers , please.
If sin A = [pic] , 0 < A < [pic] and cos B = [pic] , [pic]
7) sin (A + B)
8) cos (A – B)
9) tan (A + B )
10) 7) Verify the identity: Only work one side.
(a) [pic] (b) [pic]
Algebra 3 Trig Formulas Assignment #4
(1) Find each of the following numbers please.
(a) sin(15[pic]) (b) cos(15[pic])
© sin(105[pic]) (d) cos(75[pic])
(e) sin(195[pic]) (f) cos(165[pic])
(g) sin(345[pic]) (h) tan(15[pic])
(2) Simplify each of the following please.
(a) sin(90[pic]+ x) (b) cos(90[pic]( x)
© sin(180[pic]( x) (d) cos(180[pic]+ x)
(3) Sin(A) = [pic] , [pic], Cos(B) = [pic][pic] , [pic]. Find each of the following numbers please.
(a) sin(A + B) (b) cos(A + B)
© sin(A ( B) (d) cos(A ( B)
(e) tan(A + B) (f) csc(A ( B)
(4) Use addition or subtraction formulas to verify the identity
(a) [pic]
(b) [pic]
Assignment #4
Answers
(1) (a) [pic] (b) [pic]
(c) [pic] (d) [pic]
(e) [pic] (f) [pic]
(g) [pic] (h) [pic]
(2) (a) cos[pic] (b) sin[pic]
(c) sin[pic] (d) (cos[pic]
(3) (a) [pic] (b) - [pic]
(c) - [pic] (d) [pic]
(e) [pic] (f) [pic]
DOUBLE AND HALF ANGLE FORMULAS
Double – Angle Formulas Half – Angle Formulas
[pic] [pic]
Find each of the following numbers, please.
1) sin ( [pic])
2) cos ([pic])
If Sin A = [pic], [pic][pic] Tan B = [pic]
Find the following numbers, please.
3) sin ([pic]A)
4) cos (2B)
5) sin (A + B)
6) If [pic]is obtuse such that the [pic], find the sin 2[pic]
7) A photographer wants to take a picture of a 4’ vase standing on a 3’ pedestal. She wants to position the camera at a point C on the floor so that the angle of elevation to the top of the pedestal and the angle from the bottom of the vase to the top of the vase are the same.
How far away from the foot of the pedestal should the camera be placed?
8) Evaluate: [pic]
Algebra 3 Double and Half Angle Formulas Assignment #5
(1) Find each of the following numbers please.
(a) sin(67[pic][pic]) (b) cos(22[pic][pic])
(c) sin(112[pic][pic]) (d) cos(202[pic][pic])
(2) Sin(A) = [pic] , [pic], Tan(B) = [pic] , [pic]. Find each of the following numbers please.
(a) sin([pic]A) (b) cos([pic]A)
(c) sin([pic]B) (d) cos([pic]B)
(e) sin(2B) (f) cos(2A)
(g) sin(A ( B) (h) cos(A + B)
(3) Evaluate
(a) [pic] (b) [pic]
(4) [pic]
Answers
(1) (a) [pic] (b) [pic]
(c) [pic] (d) ([pic]
(2) (a) [pic] (b) [pic]
(c) [pic] (d) [pic]
(e) [pic] (f) [pic]
(g) [pic] (h) [pic]
(3) (a) [pic] (b) [pic]
(4) [pic]
Alg 3 Formulas Review Assign #6
(1) Find each of the following numbers please.
(a) sin(75[pic]) (b) cos(105[pic])
(c) sin[pic] (d) cos[pic]
(e) sin(195[pic]) (f) cos(285[pic])
(g) sin[pic] (h) cos[pic]
(i) sin[pic] (j) cos[pic]
(k) 2 sin[pic]cos[pic] (l) [pic] ( [pic]
(m) tan(75() (n) cos(60()
(2) Simplify each of the following please.
(a) sin(180[pic]+ x) (b) cos(90[pic]( x) (c) sin(270[pic]( x)
(d) cos(180[pic]( x) (e) sin[pic] (f) cos[pic]
(3) Sin(A) = ([pic] , [pic], Sec(B) = [pic] , [pic]. Find each of the following numbers please.
(a) sin(A + B) (b) cos(A + B) (c) sin(A ( B)
(d) cos(A ( B) (e) sin(2A) (f) cos(2A)
(g) sin(2B) (h) cos(2B) (i) sin[pic] (j) cos[pic] (k) sin[pic] (l) cos[pic]
Review Answers
(1) (a) [pic] or [pic] (b) [pic] or ([pic]
(c) [pic] or ([pic] (d) [pic] or [pic]
(e) [pic] or ([pic] (f) [pic] or [pic]
(g) [pic] (h) ( [pic]
(i) [pic] (j) [pic]
(k) [pic] or [pic] (l) [pic] or [pic]
(m) [pic] (n) [pic]
(2) (a) (sin[pic] (b) sin[pic] (c) (cos[pic] (d) (cos[pic] (e) cos(x) (f) sin(x)
(3) (a) [pic] (b) [pic] (c) [pic]
(d) [pic] (e) [pic] (f) [pic]
(g) [pic] (h) [pic] (i) [pic]
(j) ([pic] (k) [pic] (l) [pic]
7-4 through 7-5
Extra Review
1. Find each angle using angle addition/subtraction formulas
a) sin 195º b) cos 165º
2. Determine the following
a) [pic] b) [pic]
c) [pic] d) [pic]
3. [pic] Find the following. A/2 and B/2 are in Q I
a) [pic] b) [pic] c) quad of (a+b)
d) [pic] e) [pic] f) [pic]
g) [pic]
4. Find h:
ANSWERS
[pic]
[pic]
[pic]
[pic]
-----------------------
T
S
A
C
[pic]
[pic]
[pic]
[pic]
[pic]
1
60
30
1
45
45
[pic]
[pic]
15[pic]
15[pic]
[pic]"$%&*+,CDEFILMdïÝζΟ?v?\Cv?,v?,h»0¤hÞ!R5?B*CJOJ[?]QJ[?]2Θ
Θ
150
50
h
................
................
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