Trigonometry Internal - 2021

Question 1

The graphs are the same but do not intersect

Answer 1

• Both graphs have the same curve shape with maximum and minimum points increasing and decreasing
  at the same rate but never intersecting with each other. No point of intersection can be found because the graph
  of RHS is always (number) (above/below) the LHS graph
• No values of x satisfies the equation. Hence, the equation is NEVER true.

Question 2

The graphs are different but intersect

Answer 2

• The properties of (graph 1 equation) and (graph 2 equation) are different and the points of intersection occur periodically as found above in the general solutions
• The equation has periodic solutions that satisfy the equation. Hence, the equation is SOMETIMES true.

Question 3

The graphs are the same and intersect

Answer 3

• Graphically, (graph 1 equation) has the same properties as (graph 2 equation)
• Both graphs show identical properties as they are the same function.
• All values of x satisfy the equation. Hence, the equation is ALWAYS true.

Question 4

Internal Steps

Answer 4

1. Put all equations into G.C
2. Draw sketch graphs
3. Identify which equation is an identity, equation or inequation
4. List properties of each graph from equation or GC and sketch (show working)
   - Write conclusion for each equation
5. Use algebra to solve the equation (make = 0), give the general formula and general solutions
   - Write conclusion
6. Show LHS = RHS for identity
   - Write conclusion
7. Show LHS = RHS ± k for inequation
   - Write conclusion

Question 5

LHS = RHS

Answer 5

• All values of x satisfy this equation. Hence, the equation is ALWAYS true.

Question 6

LHS = RHS ± k

Answer 6

• The RHS function is the LHS function translated (vertically/horizontall) (up/down) by (amount).
• Therefore, no values of x satisfy this equation. Hence, the equation is NEVER true.

Question 7

Algebra conclusion

Answer 7

• Some values of x satisfy this equation. Hence, the equation is SOMETIMES true.