Trigonometry - CAST Flashcards
What is the purpose of using a CAST diagram in trigonometric equations?
To determine the sign of trigonometric functions in different quadrants
CAST stands for Cosine, All, Sine, Tangent, which indicates where each function is positive.
What does the acronym CAST represent?
C: Cosine positive, A: All positive, S: Sine positive, T: Tangent positive
The CAST acronym helps remember which trigonometric functions are positive in each quadrant.
In which quadrant is sine positive according to the CAST diagram?
Quadrants I and II
Sine is positive in the first quadrant (0° to 90°) and the second quadrant (90° to 180°).
In which quadrant is cosine positive according to the CAST diagram?
Quadrants I and IV
Cosine is positive in the first quadrant (0° to 90°) and the fourth quadrant (270° to 360°).
In which quadrant is tangent positive according to the CAST diagram?
Quadrants I and III
Tangent is positive in the first quadrant (0° to 90°) and the third quadrant (180° to 270°).
True or False: The CAST diagram is used to determine the sign of trigonometric functions.
True
Fill in the blank: The CAST diagram is used to solve _______ equations.
trigonometric
Solve the following trigonometric equation, for x between 0 and 360 degrees, inclusive:
sin(x) = 0.5
x = 30, and using CAST, also x = 150
What is the significance of the angles 0°, 90°, 180°, 270°, and 360° in the context of the CAST diagram?
They represent the key angles where the signs of trigonometric functions change
These angles mark the boundaries of the quadrants in the unit circle.
Solve the following trigonometric equation, for x between 0 and 360 degrees, inclusive:
tan(x) = -1
Make it positive, that is, tan(x) = 1, and recover the auxiliary/acute angle: x = 45.
Then, use CAST to work out the solutions, knowing that tan is negative in the 2nd and 4th quadrants:
x = 135 and x = 315
