Trigonometry

Question 1

How do I know whether to use Sin, Cos, or Tan?

Answer 1

S o/h C a/h T o/a

Sin Cos Tan
O pposite A djacent O pposite
H ypotenuse H ypotenuse A djacent

Question 2

What does “Adjacent” mean?

Answer 2

Adjacent means next to

Question 3

What does “Hypotenuse” mean?

Answer 3

Hypotenuse means the longest side of a right-angled triangle

Question 4

What does “Opposite” mean?

Answer 4

Opposite refers to the side of a right-angled triangle which is “opposite” the angle (θ)

Question 5

What is θ ??!?!?

Answer 5

“θ” Is a mathematical symbol which means angle

Question 6

What’s the formula to find the area of a triangle using the sine function?

Answer 6

½ ab sinC (for alex) basically it’s ½ x a x b x sinC
(C is an angle)

Question 7

What do i have to remember when finding any angle using Sin,Cos or Tan?

Answer 7

When using Sin,Tan or Cos to find a missing angle always remember it has to be ⁻¹. So for example Sin⁻¹, Cos⁻¹ or Tan⁻¹. You’re doin great alex can’t lie.

Question 8

What do you put into a calculator to find a missing side using Soh Cah Toa?

Answer 8

Ight how can I explain this.
So alex lets say you have your triangle your angle is 39°, you label your opposite side O, your Hypotenuse is 9 so the other side thats left must be A (your Adjacent side) the side you’re looking for is labelled 𝑥. Okay now imagine 𝑥 is where your adjacent side is. So boom you’ve got A (where 𝑥 was labelled) and you’ve got 9 (the side length that was given to you) which was on your hypotenuse side. WOAHHHH that’s A and H what else uses A and H???!??! THATS RIGHT Cos. Ight alex we’re almost there,

       A = 𝑥  H = 9       Now you should be thinking some like this 
                                  Your angle = 39° so you're gonna wanna realise 
                                      Cos39 = 𝑥 / 9    (𝑥 is the numerator because 𝑥   
                                         is A and 9 is your H)   now you need to re- 
                                          arrange this to help you find 𝑥. So it should 
                                           be something like  𝑥 = 9 x Cos(39°)
                                            Answer should look sum like this:
                                              6.99431365 or 7 (1 s.f.)

Question 9

What is the sine rule?

Answer 9

The Sine rule is this cool thing you can use to find a missing side or angle in trigonometry.

Question 10

What is the cosine rule?

Answer 10

The Cosine rule is this cool thing you can use to find a missing side or angle in trigonometry.

Question 11

What do I need to find a missing angle using sine rule?

Answer 11

You can perform sine rule if you have one angle and the opposite side
Extra:
If you know another angle you can work out the size of its opposite side
If you know another side, then you can work out the size of its opposite angle.

Question 12

What do I need to perform cosine rule?

Answer 12

You can use Cosine rule to find:
The length of a side if you know 2 sides and the included angle
An unknown angle if you know all 3 sides

Question 13

Why would I use sine or cosine to find a missing angle or side in a triangle?

Answer 13

Cosine and sine can be used to find a missing angle or side in non-right-angled triangle.

Question 14

What’s special about sine rule

Answer 14

It works on the basis that sinA is linked with a (the angle and its opposite side

Question 15

Sine formula for missing side

Answer 15

Formula:

    a                   b                  c
  ⸺      =      ⸺      =    ⸺
  SinA              SinB            SinC

Question 16

Sine formula for missing angle

Answer 16

Formula:

  SinA              SinB           SinC
  ⸺      =      ⸺      =    ⸺
     a                   b                 c

Question 17

Hey alex this is just to re-jiggle your memory on the sine rule
concerning angles

Answer 17

Missing angle
SinA SinB SinC
We are finding a missing angle so: ⸺ = ⸺ = ⸺
a b c
So for an angle or a side always remember:
re-jiggle memory picture (angle)

   Sinθ            Sin(112)           Now remember 8 is under Sin122  
  ⸺      =     ⸺⸺          because the angle (122°) is opposite the 
    14                   8                  side which length's 8cm this is the same 
                                               for θ (missing angle) the side opposite's 
                                               length is 14cm. Now how do I use this information to actually calculate θ???!?!? re-arrange of course! (dont forget we're finding an angle so that means we use inverse sin (sin⁻¹)) So first the re-arrangement  pretend (   is one long vertical bracket
                                                      (
          (  14 Sin(112)   )                   ( θ = sin⁻¹ ( ⸺⸺⸺ )
          (         18           )         

So essentially what’s happening is the opposite side of θ which is 14 is being added into the equation to act as if for example
in a more complicated fashion
Sinθ = Sin(112)
⸺⸺ x 14 = 0.72114.. and then after ➪ θ=sin⁻¹(0.72114..)
18 which should give something like 46° =θ

However the conclusion you must reach is that this form is much simpler and easier to follow
( 14 Sin(112) )
θ = sin⁻¹ ( ⸺⸺⸺ ) = 46° =θ
( 18 )

Question 18

Hey alex this is just to re-jiggle your memory on the sine rule concerning sides

Answer 18

Luckily this wont be as semi-confusing as working out an angle

We are finding a missing angle so: a b c
⸺ = ⸺ = ⸺
SinA SinB SinC
re-jiggle memory picture (side)
𝑥 16
⸺ = ⸺
Sin45 Sin74

Re-arrangement: 16 Sin(45)
⸺⸺⸺
Sin(74)
So in this case the opposite angle of our missing side has joined onto the front of our 16.
You should get something like
16 Sin(45)
⸺⸺⸺ = 11.76964457 = 11.8 (1 d.p)
Sin(74)

Question 19

Cosine rule formula (side)

Answer 19

When using cosine rule to find a missing side use the formula
a² = b² + c² - 2bcCosA
bruh it looks complicated but it basically means
a² = b² + c² - 2 x b x c x CosA

Question 20

Cosine rule formula(angle)

Answer 20

When using cosine rule to find a missing angle use the formula
CosA = b² + c² - a²
⸺⸺⸺
2bc

                       b² + c² - a²
 same as:     ⸺⸺⸺
                        2 x b x c