PCH5: Trigonometric Ratios

Question 1

sinø

Answer 1

opposite ÷ hypotenuse

Question 2

cosø

Answer 2

adjacent ÷ hypotenuse

Question 3

tanø

Answer 3

opposite ÷ adjacent

sinø ÷ cosø

Question 4

cosecø

Answer 4

1 ÷ sinø

Question 5

secø

Answer 5

1 ÷ cosø

Question 6

cotø

Answer 6

1 ÷ tanø
or
adjacent ÷ opposite

Question 7

What is the unit circle?

Answer 7

Circle of radius 1 unit

Question 8

When given a decimal approximation for sin/cos/tanø, how do you find the value for sin/cos/tanø

Answer 8

ø is acute. if sinø = 0.6 find cosø

sin= y= 0.6, cos= x = ?

x^2 + y^2 = 1
x^2 + (0.6)^2 = 1
x^2 + 0.36^2 = 1
x^2 = 0.64
x= 0.8 (as ø is acute, x > 0)

cosø = 0.8

Question 9

Summarise angles of any magnitude

Answer 9

1 - All +ve - ( 360˚ + ø )
2 - Sine +ve - (180˚ - ø )
3 - Tan +ve - (180˚ + ø)
4 - Cos +ve - (360˚ - ø)

Reciprocal ratios have the same signs but different values

Question 10

Describe the co-ratios

Answer 10

sin(90˚ - ø) = cosø
cos(90˚ - ø) = sinø

tan(90˚-ø) = cotø
cot(90˚-ø) = tanø

sec(90˚-ø) = cosecø
cosec(90˚-ø) = secø

Question 11

What is the formula for a trigonmetric graph?

Answer 11

a +/- sin (bx - π) +/- d
cos

a = vertical shift (+ = up, - = down)

Question 12

Pythagorean identities

Answer 12

cos^2ø + sin^2ø = 1
1 + tan^2ø = sec^2ø
cot^2ø + 1 = cosec^2ø

Question 13

Exact sine ratios

Answer 13

sin30˚ = 1 ÷ 2
sin45˚ = 1 ÷ √2
sin60˚ = √3 ÷ 2

Question 14

Exact cos ratios

Answer 14

cos30˚ = √3 ÷ 2
cos45˚ = 1 ÷ √2
cos60˚ = 1 ÷ 2

Question 15

Exact tan ratios

Answer 15

tan30˚ = 1 ÷ √3
tan45˚ = 1
tan60˚ = √3

Question 16

• True compass bearings

Answer 16

1. 0-360˚T

from north

Question 17

Angles of elevation

Answer 17

= to angles of depression

Question 18

Sine rule to find:

• Side
• Angle

Answer 18

a = b = c
—- ——- ———
sinA sinB sinC

sinA = sinB = sinC
——— ——— ———
a b c

Question 19

Cosine rule to find:

- Side

Answer 19

a^2 = b^2 + C^2 -2bc cosA
b^2 = a^2 + c^2 - 2ac cosB
c^2 = a^2 + b^2 - 2ab cosC

Question 20

Cosine rule to find:

Angle

Answer 20

cosA = b^2 + c^2 - a^2
————————–
2bc

cosB= a^2 + c^2 - b^2
————————–
2ac

cosC = a^2 + b^2 - c^2
————————–
2ab

Question 21

Area of a triangle

Answer 21

A = 0.5 ab sinC

where C is the angle included between sides A and B