Trigonometry

Question 1

Sin(pi-x) =

Answer 1

-Sin(x)

Question 2

Cos(2pi - x) =

Answer 2

Cos(x)

Question 3

Sin(90-x) =

Answer 3

Cos(x)

Question 4

Period of sin = Period of cos =

Answer 4

2*pi

Question 5

Period of tan =

Answer 5

pi

tan(1.25pi) = tan(0.25pi)

Question 6

Not all values of theta if and only if

Answer 6

dividing by zero

Question 7

radians > degrees

Answer 7

ranges of trig

Question 8

3sin^2(x) + 2sinxcosx + cos^2x =

Answer 8

3tan^2x + 2tanx + 1

Question 9

How many solutions to (3+cosx)^2 = 4-2sin^8x

Answer 9

LHS range is 4-16
RHS range is 2-4
Therefore one solution when x=4

Question 10

Consider the range of the trig functions

Answer 10

-1 - 1

0 - 1

Question 11

Divided by sin/cos/sin^2x/cos^2x

Answer 11

to find a quadratic

Question 12

Sin^n(a) range changes only when

Answer 12

n=2x not when a changes

Question 13

Cos(2pi - x) =

Answer 13

cosx = sin(90 - x)

Question 14

(3+cosx)^2 = 4-sin^8(x)

Answer 14

LHS varies from 4-16
RHS varies from 2-4
therefore only one solution of 4

Question 15

sin(pi - x) =

Answer 15

sin(-x) = -sin(x)

Question 16

max/min of trig:

Answer 16

0 < (3sin^2(7x+11)) < 3

Question 17

Trig has multiple solutions –>

Answer 17

check domain

Question 18

Simultaneous equations with trig –>

Answer 18

think of identities

Question 19

Trig equalities: simplify, think of ranges + identities

Answer 19

2^(-x^2), 2^(2x-x^2) stationary point

Question 20

tanX = q/p

Answer 20

p^2 - 4pq + q^2 = 0

(p/q)^2 - 4(p/q) + 1 = 0

Question 21

Two solutions for trig, sin2x…

Answer 21

When relating angles/lengths use shared lengths/angles

Question 22

trig –> ranges

Answer 22

CosX, sinX –> cosXCosX + sinXSInX = 1

Question 23

sin^2(x) + 3sinxcosx + 2cos^2x = 0

Answer 23

cosx =/= 0 therefore divide by cos^2(x)

tan^2(x) + 3tanx(x) + 2 = 0

Question 24

sin(x) < x

Answer 24

check domains for amounts of solutions