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, 495
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 (calc)
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
Solve sin (2x - 20) = 0.5, 0 < x < 360
x = 25, 85, 205, 265
pi radians in degrees
180
Maximum value on a trig graph
Largest value
Minimum valence on a trig graph
Smallest value
Period
Length of one cycle of the wave
Length of one cycle of the wave
Period
Amplitude
Distance from middle of graph to top of graph
Distance from middle of graph to top of graph
Amplitude
Exact value triangles
