Addition and Subtraction Formulas

ALG 3/TRIG(10)1

ADDITION AND SUBTRACTION FORMULAS

sin = sincos + cossin

sin = sincos - cossin

cos = coscos - sin sin

cos = coscos + sinsin

tan =

COMBINATIONS

15 = 345 =

255 = 75 =

EXAMPLES

Evaluate each expression

1) sin 75

2) cos 345

3) tan 165

Simplify the following:

4) cos (270 - x)

5) sin ( x + ) =

6) cos ( )

Find each of the following numbers , please.

If sin A = , 0 < A < and cos B = ,

7) sin (A + B)

8) cos (A – B)

9) tan (A + B )

10) 7) Verify the identity: Only work one side.

(a) (b)
Algebra 3 Trig Formulas Assignment #4

(1) Find each of the following numbers please.

(a) sin(15)(b) cos(15)

(e) sin(195)(f) cos(165)

(g) sin(345)(h) tan(15)

(2) Simplify each of the following please.

(a) sin(90+ x)(b) cos(90 x)

(3) Sin(A) = , , Cos(B) = , . Find each of the following numbers please.

(a) sin(A + B)(b) cos(A + B)

(e) tan(A + B)(f) csc(A  B)

(4) Use addition or subtraction formulas to verify the identity

(a)

(b)

Assignment #4

Answers

(1)(a) (b)

(e) (f)

(g) (h)

(2)(a) cos(b) sin

(3) (a) (b) -

(e) (f)

DOUBLE AND HALF ANGLE FORMULAS

Double – Angle Formulas Half – Angle Formulas

Find each of the following numbers, please.

1) sin ( )

2) cos ()

If Sin A = , Tan B =

Find the following numbers, please.

3) sin (A)

4) cos (2B)

5) sin (A + B)

6) If is obtuse such that the , find the sin 2

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:
Algebra 3 Double and Half Angle Formulas Assignment #5

(1) Find each of the following numbers please.

(a) sin(67)(b) cos(22)

(2) Sin(A) = , , Tan(B) = , . Find each of the following numbers please.

(a) sin(A)(b) cos(A)

(e) sin(2B)(f) cos(2A)

(g) sin(A  B)(h) cos(A + B)

(3) Evaluate

(a) (b)

(4)

Answers

(1)(a) (b)

(2) (a) (b)

(c)(d)

(e) (f)

(g)(h)

(3) (a) (b)

(4)

Alg 3 Formulas Review Assign #6

(1) Find each of the following numbers please.

(a) sin(75)(b) cos(105)

(e) sin(195)(f) cos(285)

(g) sin(h) cos

(i) sin(j) cos

(k) 2 sincos(l) 

(m) tan(75)(n) cos(60)

(2) Simplify each of the following please.

(a) sin(180+ x)(b) cos(90 x) (c) sin(270 x)

(d) cos(180 x)(e) sin (f) cos

(3) Sin(A) =  , , Sec(B) = , . 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 (j) cos (k) sin (l) cos

Review Answers

(1) (a) or (b) or 

(e) or (f) or

(g) (h) 

(i) (j)

(k) or (l) or

(m) (n)

(2)(a) sin(b) sin (c) cos (d)cos (e) cos(x) (f) sin(x)

(3) (a) (b) (c)

(d)(e) (f)

(g) (h) (i)

(j) (k) (l)

7-4 through 7-5

Extra Review

1. Find each angle using angle addition/subtraction formulas

a) sin 195ºb) cos 165º

2. Determine the following

a) b)

c) d)

3. Find the following. A/2 and B/2 are in Q I

a) b) c) quad of (a+b)

d) e) f)

4. Find h:

ANSWERS