Trigonometry

Question 2

Length of Line

Question 3

Midpoint of Two Points

Answer 3

Question 4

Pythagorean Theorem in terms of

sin & cos

Answer 4

sin²x + cos²x = 1

tan²x + 1 = sec²x

cot²x + 1 = csc²x

Question 5

even and odd f(-x) = -f(x)

Answer 5

cos(-t) = cos t ; sec (-t) = sec t EVEN

sin (-t) = -sin t ; csc(-t) = -csc t ODD

tan (-t) = -tan t ; cot (-t) = -cot t ODD

Question 6

Graph of y = sin x

Answer 6

Question 7

Graph of y = cos x

Answer 7

Question 8

Amplitude and Period

Answer 8

y = A sin (w x) & y = A cos (w x)

                                                      IAI = amplitude

                                                                 &

                                                            2π/w = period

Question 9

Graph of y = tan x

Answer 9

Question 10

Graph of y = cot x

Answer 10

Question 11

Graph of y = csc x

Answer 11

Question 12

Graph of y = sec x

Answer 12

Question 13

Domain and Range

sin(sin^-1x) = x

sin^-1(sin x) = x

Answer 13

sin(sin^-1x) = x ; x –> [-1,1]

                                                                                   sin<sup>-1</sup>(sin x)  =  x  ;  x --\> [-π/2 , π/2]

Question 14

Domain and Range

cos(cos^-1x) = x

cos^-1(cos x) = x

Answer 14

cos(cos^-1x) = x ——–> x -> [-1,1]

cos^-1(cos x) = x ——–> x -> [0,π]

sin-1 = y sin y = 1

Question 15

Domain and Range

tan(tan^-1 x) = x

tan^-1(tan x) = x

Answer 15

tan(tan^-1 x) = x ———> x -> all reals

tan^-1(tan x) = x ———-> x -> [-π/2 , π/2]

Question 16

A/B = C/D Then….

Answer 16

AD = BC

Question 17

(a²-b²) ===

(a³-b³) ===

(a⁴-b⁴) ===

Answer 17

(a²-b²) = (a+b)(a-b)

(a³-b³) = (a-b)(a²+ab+b²)

(a⁴-b⁴) = (a-b)(a+b)(a²+b²)

Question 18

Sum & Difference

cos (a+b)

cos (a-b)

Answer 18

cos (a+b) = (cos a)(cos b) - (sin a)(sin b)

cos (a-b) = (cos a)(cos b) + (sin a)(sin b)

Question 19

Sum and Difference

sin (a+b)    

sin (a-b)

Answer 19

sin (a+b) = (sin a)(cos b) + (sin b)(cos a)

sin (a-b) = (sin a)(cos b) - (sin b)(cos a)

Question 20

Sum and Differnce

tan (x+y)

tan (x-y)

Answer 20

Question 21

Double Angle

sin (2a) =

cos (2a) =

cos (2a) =

cos (2a) =

tan (2a) =

Answer 21

sin (2a) = (2sin a)(cos a)

cos (2a) = cos²a - sin²a

cos (2a) = 1 - 2sin² a

cos (2a) = 2cos² a - 1

tan (2a) =

Question 22

Half Angle

sin (a/2) ===

cos (a/2) ===

tan (a/2) ===

Answer 22

Question 23

Product - to - Sum Formulas

(cos a)(cos b) =

(sin a)(sin b) =

Answer 23

Question 24

Sum - to - Product formula

sin a + sin b =

sin a - sin b =

Answer 24

Question 25

Unit Circle BITCH

Answer 25

Question 26

Product - to - Sum

(sin a)(cos b) =

(cos a)(sin b) =

Answer 26

Question 27

Sum - to - Product Formula

cos a + cos b =

cos a - cos b =

tan a + tan b =

Answer 27