IM STUCK ON THESE :(
1. What is the equation for shifting the standard sine curve +2 units horizontally?
A. y = sin (x + 2)
B. y = sin x + 2
C. y = sin x − 2
D. y = sin (x − 2)
3. What is tan-¹ √3/3 ?
A. π/4
B. -π/3
C. π/6
D. -π/4
4. cot–1 −0.57735 is approximately
A. −0.65.
B. −1.05.
C. 2.62.
D. 2.09.
5. What is the period of y=√3sin(1/3x-1/3)?
A. 6π
B. π/3
C. √3π
10. 16. Which of these statements are true??
(i) The domain of the inverse cosine function (y = cos–1 x) is –1 ≤ x ≤ 1.
(ii) The range of the inverse sine function (y = sin–1 x) is 0 ≤ y ≤ p.
(iii) The range of the inverse tangent function (y = tan–1 x) is –p/2 < y < p/2.
A. (i) and (ii)
B. (i), (ii), and (iii)
C. (ii) and (iii)
D. (i) and (iii)
11. What is the frequency of y=tan(π/3x)
A. 1/3
B. 3
C. 1/6
14. How many solutions does the system y=x
y=tan x have?
A. Infinitely many
B. 3
C. None
1. (D)
3. (C)
4. (B) −0.57735 is -1/√3
5. (A) 2pi/(1/3) = 6pi
10. (D)
11. (C) 1/(2pi/(pi/3))
14. (A)
1. To shift the standard sine curve +2 units horizontally, you need to subtract 2 from the x-coordinate. The correct equation is D. y = sin (x − 2).
3. To find tan-¹ √3/3, you need to find the angle whose tangent is equal to √3/3. The correct answer is C. π/6.
4. To find cot–1 −0.57735, you need to find the angle whose cotangent is -0.57735. The correct answer is A. -0.65.
5. To find the period of y=√3sin(1/3x-1/3), you need to determine the value that scales the x-coordinate. The equation is in the form y = A*sin(Bx + C), where B determines the period. In this case, B = 1/3, so the period is 2π/|B| = 2π/|1/3| = 6π. The correct answer is A. 6π.
10. The correct statements are (ii) and (iii). For the inverse sine function (y = sin⁻¹x), the range is -π/2 ≤ y ≤ π/2. For the inverse tangent function (y = tan⁻¹x), the range is -π/2 < y < π/2. So, the correct answer is C. (ii) and (iii).
11. To find the frequency of y = tan(π/3x), you need to determine the scaling factor of the x-coordinate. In this case, the frequency is the reciprocal of the coefficient of x, which is 3. The correct answer is B. 3.
14. The system y = x, y = tan x has infinitely many solutions. If you graph both equations, you'll see that the line y = x intersects the graph of y = tan x at multiple points. The correct answer is A. Infinitely many.