Trig Flashcards
(20 cards)
What is the sine rule?
a/sinA = b/sinB = c/sinC
What is the cosine rule?
c² = a² + b² - 2ab cosC
When do you use the sine rule?
When you have ASA or AAS or two sides and a non-included angle.
When do you use the cosine rule?
When you have SAS or SSS.
What is the formula for the area of a triangle using trigonometry?
Area = 1/2 ab sinC
What is the domain of sin(x)?
All real numbers.
What is the range of sin(x)?
[-1, 1]
What is the period of sin(x) and cos(x)?
360° or 2π radians.
What is the period of tan(x)?
180° or π radians.
What is the range of tan(x)?
All real numbers except odd multiples of 90° or π/2.
What does the graph of y = sin(x) look like?
A smooth periodic wave oscillating between -1 and 1.
What transformation is applied in y = sin(2x)?
Horizontal compression by a factor of 1/2.
What transformation is applied in y = 2sin(x)?
Vertical stretch by a factor of 2.
What is the amplitude of y = 3cos(x)?
3
How do you solve sin(x) = 0.5 for 0° ≤ x ≤ 360°?
x = 30°, 150°
How do you find general solutions to trig equations?
Add periodic multiples (e.g., x = θ + 360n for sin/cos, 180n for tan).
What are the exact values for sin(30°), cos(60°), and tan(45°)?
1/2, 1/2, and 1
What is the identity for sin²x + cos²x?
sin²x + cos²x = 1
What is the identity for tan(x)?
tan(x) = sin(x)/cos(x)
What are the key features of the graph of y = tan(x)?
Vertical asymptotes at x = 90°, 270°, etc., and periodic with period 180°.
