Math 4 Unit 4 TEST

The amplitude of a cosine function is the maximum distance from the midline of the graph to its peak. For f(x) = A cos(x), the amplitude is |A|.

sin 30 degrees = 1/2.

To find the value of x, isolate x using algebraic methods and apply inverse trigonometric functions if necessary.

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of a leg.

The general form of a sine function is y = A sin(Bx + C) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

The period of y = sin x is 2π.

The phase shift can be determined from the equation y = A sin(B(x - C)) + D, where C/B gives the phase shift.

Sine and cosine are co-functions: sin(x) = cos(90° - x) and cos(x) = sin(90° - x).

The Pythagorean identity states that sin²(x) + cos²(x) = 1.

The amplitude is the absolute value of the coefficient of the cosine function, so for f(x) = -3cos x, the amplitude is 3.