Chap. 7 - Trigonometry

Question 1

sine ratio

Answer 1

o/h

Question 2

cos ration

Answer 2

a/h

Question 3

tan ratio

Answer 3

o/a

Question 4

how do you calculate unknown angles using a calculator

Answer 4

put the fraction / number into the inverse of the ratio
e.g sin(theta) = 1/2
theta = sin^-1(1/2)

Question 5

in terms of linear relationships, how do you calculate the gradient using trigonometry?

Answer 5

tan(theta) = m (the gradient)

Question 6

what is the angle of inclination in linear relationships

Answer 6

between a line and the positive direction of the x-axis

Question 7

The angle of elevation is measured

Answer 7

up from the horizontal

Question 8

The angle of depression is measured

Answer 8

down from the horizontal

Question 9

true bearings are measured:

Answer 9

clockwise from the northline

Question 10

to find the answer in a bearings question, the first step (in evie’s brain) is to

Answer 10

MAKE A GRAPH!!!!!!!!

Question 11

two tips for trig in 3d ARE

Answer 11

• draw a careful diagram with all right angled triangles marked
• top down view can help

Question 12

sin30 =

Answer 12

1/2

Question 13

sin 60 =

Answer 13

√3 / 2

Question 14

cos30

Answer 14

√3 / 2

Question 15

cos60

Answer 15

1/2

Question 16

tan30

Answer 16

1 / √3

Question 17

tan60

Answer 17

√3

Question 18

angles in the 1st quadrant are always:

Answer 18

acute

Question 19

sin(theta) = cos…

Answer 19

(90 - theta)

Question 20

angles in the 2nd quadrant are always

Answer 20

obtuse

Question 21

cos(180° − θ) =

Answer 21

−cos θ

Question 22

sin(180° − θ) =

Answer 22

sin θ

Question 23

tan(180° − θ) =

Answer 23

−tan θ

Question 24

the sine rule is

Answer 24

a/sinA = b/sinB = c/sinC

Question 25

the sine rule is used when

Answer 25

when we are given either a) two angles and one side, or b) two sides and a non-included angle

Question 26

the ambiguoes case exists when

Answer 26

*you're using the sine rule *you're finding an angle *the given angle is acute *the sum of the two possible answers does not exceed 180°

Question 27

use the cosine rule when

Answer 27

*given 3 sides of a triangle *given 2 sides and an included angle

Question 28

side a and b are adjacent to

Answer 28

angle C

Question 29

area of a triangle is given by:

Answer 29

A=1/2*ab*sinC

Question 30

to complete area of a triangle you need

Answer 30

two sides and a given angle

Question 31

what is the related angle

Answer 31

the angle between the x axis and the hypotenuse of the triangle

Question 32

explain the ALL STATIONS TO CENTRAL nemonic

Answer 32

A = all positive S = only sin is positive T = only tan is positive c = only cos is positive

Question 33

what does the related angle do?

Answer 33

it helps you find sin, cos and tan theta for any size

Question 34

how do you evaluate angles of any magnitude using the related angle?

Answer 34

1. determine which quadrant the new angle is in 2. determine the size of the related angle using the quadrant location 3. establish your answer as positive or negative 4. using special triangles, put the answer in integer form if possible, (e.g -tan45 = -1)

Question 35

ASK MR DELHORY ABOUT BOUNDARY ANGLES!!!!!!!