Triganometry

Question 1

What are the five rules to know for trigonometry?

Answer 1

Only works on right angled triangles
Hypotenuse is the length opposite the right angle
0=theta, an angle in the triangle (not the right angle
Opposite is the length opposite 0
Adjacent is the side adjacent to 0, but not the hypotenuse

Question 2

Adjacent means what?

Answer 2

Next to

Question 3

Sin 0 = ?

Answer 3

Opposite / Hypotenuse

Question 4

Cos 0 = ?

Answer 4

Adjacent / Hypotenuse

Question 5

Tan 0 = ?

Answer 5

opposite / Hypotenuse

Question 6

What does ‘sin’ stand for?

Answer 6

Sine

Question 7

What does ‘cos’ stand for?

Answer 7

Cosine

Question 8

What does ‘tan’ stand for?

Answer 8

Tangent

Question 9

What are the two ways to remember trigonometry equations?

Answer 9

Smiles or happiness come after drinking tonnes of alcohol

SOHCAHTOA

Question 10

|. \
|. \10cm
x|. \
|___60*__\

Which trigonometry equation would you use?

Answer 10

Theta = 40*
Opp=x
Hyp=10cm
Adj= —-

Sin = opp/adj

Question 11

|. \
|. \10cm
x|. \
|___60*__\

Work out the length AB

Answer 11

Sin 0 = opp/hyp
(Substitute in knowns)
Sin 60 = x/10
/x10
10xsin60= x
(Enter it into the calculator as Sin(60) x 10
8.6602=x
8.7cm=x

Question 12

|60*\
  |.        \
x|.           \
  |\_\_\_\_\_\_\_\_\_\
       8cm

Work out the length AB

Answer 12

Tan 0 = opp/adj
Tan 0=8cm/x
/xX
X x tan60 = 8
/divide by tan60
X=8/tan60
(Calculator: 8/tan(60)
X=4.62cm

Question 13

ABC IS a right angled triangle. Length AC is 12cm. Length AB is 6cm. Find angle BAC.

    | \ 6cm|.     \12cm
    |.          \
    |\_\_\_\_\_\_\_\_\_\_\

Answer 13

Cos 0 = adj/hyp
Cos0 = 6/12
/cos^-1
0=cos^-1 (6/12)
0=60

Question 14

Sin theta 0* = ?

Answer 14

0

Question 15

Sin theta 30* = ?

Answer 15

1/2

Question 16

Sin theta 45* = ?

Answer 16

1/(square root of 2) - (square root of 2)/2

Question 17

Sin theta 60* = ?

Answer 17

(Square root of 3)/2

Question 18

Sin theta 90* = ?

Answer 18

1

Question 19

Cos theta 0* = ?

Answer 19

1

Question 20

Cos theta 30* = ?

Answer 20

(Square root 3)/2

Question 21

Cos theta 30* = ?

Answer 21

(Square root 3)/2

Question 22

Cos theta 45* = ?

Answer 22

1/(square root 2) - (square root 2)/2

Question 23

Cos theta 60* = ?

Answer 23

1/2

Question 24

Cos theta 90* = ?

Answer 24

0

Question 25

Tan theta 0* = ?

Answer 25

0

Question 26

Tan theta 30* = ?

Answer 26

1/(square root 3)

Question 27

Tan theta 45* = ?

Answer 27

1

Question 28

Tan theta 60* = ?

Answer 28

Square root 3

Question 29

Tan theta 90* = ?

Answer 29

Error

Question 30

What is the exact value for 6cos 30*?

Answer 30

=6x(square root 3)/2
=6(square root 3)/2
=3(square root 3)/1

Question 31

What is the exact value of 8x1/(square root 2)

Answer 31

=8/1x1/(square root 2)
=8/(square root 2)
/x square root 2
=8(square root 2)/2
=4(square root 2)

Question 32

ABC is a right angled triangle. Length AC is 12cm. Length AB is 6cm. Find angle BAC.

Answer 32

Cos 0 = adj/hyp
Cos 0=6/12
/cos ^-1
0=cos ^-1 (6/12)
0=60*

(Cos is a function not a number. Cos ^-1 is undoing this function.)

Question 33

Work out value of x
   12cm   /.  | xcm
            /.      |
        /.30*   | (right angle)
       ---------

Answer 33

Sin 0=opp/hyp
Sin 30=x/12
/x12
12xsin30= x
=12x1/2= x
=6 = x

Question 34

What is the sine rule?

Answer 34

sinA/a = sinB/b = sinC/c OR a/sinA = b/sinB = c/sinC

Question 35

What is the cosine rule?

Answer 35

a^2 = b^2 + c^2 - 2bccosA