What is the period of y = �ã3sin (1/3x-�ã1/3)?
A, 6ƒÎ
B. �ã3ƒÎ
C, 2ƒÎ/3
D. ƒÎ/3
What is tan^-1 �ã3/3?
A. ƒÎ/6
B. ƒÎ/4
C. -ƒÎ/3
D. -ƒÎ/4
What is the frequency of y = tan (ƒÎ/3 x) ?
A. 3
B. 1/6
C. ƒÎ/3
D. 1/3
What is the amplitude of y = 1/5 sin (�ã5x+1/�ã5)?
A. �ã5
B. 1/5
C. 1/�ã5
D. �ã5ƒÎ
To find the period of a sine function in the form y = A*sin(Bx + C), we can use the formula T = 2π/|B|, where T is the period.
For the first question, we have y = �ã3sin(1/3x - �ã1/3). Comparing this to the standard form, we see that B = 1/3. Applying the formula, we get T = 2π/|1/3| = 2π*3 = 6π. Therefore, the correct answer is A, 6π.
To find the value of tan^-1 (arctan), we need to use the inverse trigonometric function. The arctan of a number is the angle whose tangent is equal to that number.
For the second question, we have tan^-1(�ã3/3). To find this value, you can use a calculator or reference table to determine the angle whose tangent is equal to �ã3/3. In this case, the correct answer is B, ƒÎ/4.
To find the frequency of a tangent function in the form y = tan(Ax), we can use the formula f = 1/|A|, where f is the frequency.
For the third question, we have y = tan(ƒÎ/3x). Comparing this to the standard form, we see that A = ƒÎ/3. Applying the formula, we get f = 1/|ƒÎ/3| = 3/ƒÎ. Therefore, the correct answer is A, 3.
To find the amplitude of a sine function in the form y = A*sin(Bx + C) or cosine function y = A*cos(Bx + C), the amplitude is defined as the absolute value of A.
For the fourth question, we have y = 1/5sin(�ã5x + 1/�ã5). Comparing this to the standard form, we see that A = 1/5. Therefore, the correct answer is B, 1/5.