Trig. Ratios, Identities & Equations (P1.9 & 1.10)

Question 1

what version of the cosine rule is used to find a missing side?

Answer 1

a^2 = b^2 + c^2 -2bc.cosA

Question 2

what version of the cosine rule is used to find a missing angle? (must know all 3 sides)

Answer 2

cosA = b^2 + c^2 - a^2 / 2bc

Question 3

prove the cosine rule

Answer 3

see pg 174 P1 textbook

Question 4

what version of the sine rule is used to find the length of a missing side?

Answer 4

a/sinA = b/sinB = c/sinC

Question 5

what version of the sine rule is used to find a missing angle?

Answer 5

sinA/a = sinB/b = sinC/c

Question 6

prove the sine rule

Answer 6

see p179 P1 textbook

Question 7

the sine rule sometimes produces 2 possible solutions for a missing angle

Answer 7

for given side lengths b & c & given angle B, you can draw the triangle in 2 different ways - such that angle C is obtuse or acute
sinθ = sin(180-θ)

Question 8

state the formula for the area of a triangle when you know 2 sides & the angle b/w them

Answer 8

A = 1/2absinC

Question 9

solving triangle problems

Answer 9

using sine, cosine Pythagoras & right-angles trig.

Question 10

the graphs of sine, cosine & tangent are periodic

Answer 10

they repeat themselves after a certain interval

Question 11

describe the graph of y = sinθ

Answer 11

repeats every 360degrees
intersects x-axis at -180, 0, 180, 360 etc.
max. 1 & min. -1

Question 12

describe the graph of y = cosθ

Answer 12

repeats every 360degrees
intersects x-axis at -90, 90, 270, 450 etc.
max. 1 & min. -1

Question 13

describe the graph of y = tanθ

Answer 13

repeats every 180degrees
intersects x-axis at -180, 0, 180, 360 etc.
no max. or min.
vertical asymptotes at x=-90, 90, 270

Question 14

transforming trig. graphs

Answer 14

just practice

Question 15

describe how a unit circle with centre at origin can be used to understand trig. ratios

Answer 15

for a point P(x,y) on a unit circle such that OP makes angleθ with the +ve x-axis:
cosθ = x (x-coordinate of P)
sinθ = y (y-coordinate of P)
tanθ = y/x (gradient of OP)

Question 16

how must you measure positive angles?

Answer 16

anticlockwise from +ve x-axis

Question 17

how do you measure negative angles?

Answer 17

clockwise from +ve x-axis

Question 18

describe how the x-y plane is divided into quadrants & what the angles are for each quadrant

Answer 18

see pg 205 P1 textbook

Question 19

describe CAST diagram

Answer 19

reference pg 205-6 P1 textbook

Question 20

describe how to find exact values of trig. ratios by considering triangles

Answer 20

equilateral triangle with sides of length 2 units:
perpendicular from A to meat BC at D
apply trig. ratios in the right-angled triangle ABD

isosceles right-angled triangle PQR with PQ = RQ = 1 unit

see pg208 P1 textbook

Question 21

sin^2θ + cos^2θ =

Answer 21

1

Question 22

tanθ =

Answer 22

sinθ / cosθ
undefined when cosθ = 0 (when θ = -90, 90, 270…)

Question 23

solve equations in the form sinnθ = k, cosnθ = k & tannθ = k

Answer 23

calculator gives principle values (in range -90 - 90)
change range
sketch curve in given range
find solutions
then divide by n to get θ

Question 24

solve equations in the form sinθ = cosθ

Answer 24

it is always okay to divide by cosθ to get tanθ =

Question 25

solving quadratics in sinθ, cosθ & tanθ