5. Trig Equations Flashcards
Method for basic trig equations
- Rearrange so operation (cos, tan, sin) is on its own
- Use triangles
- CAST
Solve 4 cosx - 5 = -3, 0 < x < 360
x = 60, 300
solve /2 sinx - 1 = 0, 0 < x < 720
x = 45, 135, 405, 720
What to do when interval is >360
Add 360 to solutions until it exceeds 720
Method when there is a multiple angle
- Alter the interval
- Calculate the first 2 values
- Find all values by +360, remaining within interval
- Divide answers so left with x = solutions
- Alter the interval
- Calculate the first 2 values
- Find all values by +360, remaining within interval
- Divide answers so left with x = solutions
Method when there is a multiple angle
Multiple angle =
Number in front of x
Solve sin3x = -0.8, 0 < 3x < 360. calculator
77.7, 102.3, 197.7, 223.3, 317.7, 342.3
Solve 4 = 5 - tan2x, 0 < x < 360
x = 22.5, 112.5, 202.5, 292.5
Solve 4cos^2x - 5 = -2, 0 < x < 360
x = 30, 150, 210, 330
What to do if operation (cos, tan, sin) is both +ive and -ive
Use all four quadrants
When is a operation (cos, tan, sin) both positive and negative
When it is equal to a square root
Solve 4sin^2x + 11sinx + 6 = 0
228.59, 311.41
Solve 2cos^2x = 5 - 7sinx, 0 < x < 360
x = 30 or 150
Sin and cos relationships
sin^2x + cos^2x = 1
sin^2x = 1 - cos^2x
cos^2x = 1 - sin^2x
Exact value triangles
