Unit 2 - Trigonometry

Question 1

What are the trigonometric ratios, and what type of triangle do they work for?
2.1

Answer 1

Acronym: SOH CAH TOA
Sin θ = Opp/Hyp
Cos θ = Adj/Hyp
Tan θ = Opp/Adj

RATIOS CAN ONLY BE USED FOR RIGHT ANGLES

θ = Unknown angle (x but for angles)

Hypotenuse = across from 90 degree angle (longest side)
Opposite = across from theta
Adjacent = next to angle (remaining side)

Question 2

How to solve trig problems (solve for a side length with another side length and an angle)?
2.1

Answer 2

1. Complete the context (label sides)
   *Note: If this step is incorrect, the whole problem will be incorrect
2. Choose the appropriate ratio (either SIN/COS/TAN)
3. Solve for unknown
   *Make sure your calculator is in degrees
   3a. Substitute
   3b. Isolate variable
   3c. Solve
   3d. Round

Question 3

To solve for a triangle means:
2.2

Answer 3

to solve for every length and every angle in a triangle

Question 4

How to find angles?
2.2

Answer 4

1 Complete the context (label sides)
2. Choose the appropriate ratio (either SIN/COS/TAN)
3. Write out ratio of theta: Ratio θ = __/__
4. Multiply both sides by the inverse of that ratio to get rid of it: Ratio -1 x Ratio θ = (__/___) x Ratio -1

*May also be able to use Pythagorus theorum, a^2 + b^2 = c^2, (Note: Hypotenouse is always C).
Or, all angles add up to 180, so if you have 90 degrees and another known angle, you can solve for the final one.

Question 5

Isosceles triangles
2.3

Answer 5

• If you have an isosceles triangle, it is equal, and you can draw a line down the middle and make two right angled triangles

Question 6

Circles
Tangents
2.3

Answer 6

• If you have two radius (middle of circle to edge) as long as they are the same side of the circle, when you connect them you get a cord. If you have a cord, you can connect them back to the center of the cirlce.
• Tangent: a line that hits the outside of a circle at one particular spot at 90 degrees to the center of the circle. Tangent means you can create a right angle triangle.

Question 7

How to problem solve?
2.3

Answer 7

1. Draw a diagram
2. Complete the context (label sides)
3. Locate the right angle
4. Choose an appropriate ratio (Sin/Cos/Tan)
5. Solve for unknown
6. *Write answer in sentence form

Question 8

3D problem solving
2.4

Answer 8

• Use the same trigonometric ratios (Sin/Cos/Tan) and Pythagorus theorem (a^2+b^2=c^2, where c is the hypotenuse) to find diagonals of shapes

Question 9

What is the sine rule and when do we use it?
2.5

Answer 9

Sin A/a = Sin B/b = Sin C/c

OR a/Sin A = B/Sin b = C/Sin c

To use the Sine rule, one complete set of information is required (Sin A & a or Sin B & b or Sin C & c), plus another side length or angle

The variable representing the letter represents the opposite side length

Question 10

What are the cos rules and when do you use them?
2.6

Answer 10

a^2 = b^2 + c^2 - 2bc cos A
b^2 = a^2 + c^2 - 2ac Cos B
c^2 = a^2 + b^2 - 2ab Cos C

• You need two side lengths and an angle in between (S.A.S) to solve for the third length

Cos A = (b^2 + c^2 - a^2)/2bc
- All 3 side lengths are required for this rule