MATH 111 – Week 5 – Trigonometric Formulas and Equations
Need help with your assignment ? Reach out to us. We offer excellent services.
1. Which solution describes every angle that has a $\frac{π}{3}$ reference angle in the first quadrant? (Note that n is an integer.)
- $\frac{π}{3}$
- $\frac{π}{6}$ + n
- $\frac{π}{3}$ + n
- $\frac{π}{3}$ + πn
- $\frac{π}{3}$ + 2πn
2. Which solution describes every angle that has a 25˚ reference angle in the second or fourth quadrant?
- 25˚
- 25˚ + n
- 155˚ + 90n
- 155˚ + 180n
- 155˚ + 360n
3. Solve for x in 2sinx = 1.
- 60˚
- 30˚
- -30˚
- -60˚
- There is no answer.
4. Solve for x in 2sinx = 1 when x is between 0˚ and -180˚.
- 60˚
- 30˚
- -30˚
- -60˚
- There is no answer.
5. Solve for x in 2sinx = -1.
- 60˚
- 30˚
- -30˚
- -60˚
- There is no answer.
6. Solve for x in 2sinx = -1 when x is between -90˚ and -180˚.
- -30˚
- -60˚
- -120˚
- -150˚
- There is no answer.
7. Solve for x in 2sinx = -1 when x is between 90˚ and 270˚.
- 30˚
- 60˚
- 210˚
- 240˚
- 330˚
8. Which answer is a solution to the equation 2cosx = 0?
- $\frac{π}{2}$
- $\frac{π}{3}$
- $\frac{π}{4}$
- $\frac{π}{6}$
- π
9. Solve for x in 3cosx = 0 when x is between π and 2π.
- π
- 2π
- $\frac{π}{2}$
- $\frac{2π}{3}$
- $\frac{3π}{2}$
10. Solve for x in sin$^{2}$x = sinx.
- x = 0
- x = $\frac{π}{4}$
- x = $\frac{π}{2}$
- x = 0, x = $\frac{π}{2}$
- x = $\frac{π}{2}$, x = $\frac{π}{4}$
11. Solve for x in sin$^{2}$x = -sinx.
- x = 0
- x = $\frac{π}{2}$
- x = $-\frac{π}{2}$
- x = 0, x = $\frac{π}{2}$
- x = 0, x = $-\frac{π}{2}$
12. Solve for x in sin$^{2}$x = -sinx when $\frac{π}{2}$ ≤ x ≤ $\frac{3π}{2}$.
- x = $\frac{π}{2}$
- x = $\frac{-π}{2}$
- x = $\frac{3π}{2}$
- x = π, x = $\frac{3π}{2}$
- x = $\frac{π}{2}$, x = $-\frac{π}{2}$
13. Solve for x in sin$^{2}$x = sinx when 0 ≤ x ≤ -π.
- x = 0
- x = $-\frac{π}{2}$
- x = -π
- x = 0, x = -π
- x = 0, x = $-\frac{π}{2}$
14. Solve for x in 2sin$^{2}$x $-$ 1 = sin$^{2}$x.
- x = 0˚
- x = 60˚
- x = 120˚
- x = 0˚, x = 30˚
- x = -90˚, x = 90˚
15. Solve for x in sin$^{2}$x $-$ 2 = -sinx when x is between 0˚ and 180˚
- x = 30˚
- x = 90˚
- x = 150˚
- x = 0˚, x = 120˚
- x = -30˚, x = 60˚
16. Solve for x in 4sin$^{2}$x + 3sinx + 2 = -3sinx.
- x = 0
- x = $-\frac{π}{3}$
- x = $\frac{5π}{6}$
- x = $\frac{2π}{3}$, x = π
- x = $-\frac{π}{6}$, x = $-\frac{π}{2}$
17. Solve for x in 4sin$^{2}$x + 3sinx + 2 = -3sinx when 90˚ ≤ x ≤ 270˚.
- x = 90˚
- x = 150˚
- x = 270˚
- x = 0˚, x = 90˚
- x = 210˚, x = 270˚
18. Simplify sin(165˚).
- -0.64
- -0.26
- 0
- 0.26
- 0.64
19. If sin$\bigl(\frac{π}{16}\bigr)$ = 0.1951 and cos$\bigl(\frac{π}{16}\bigr)$ = 0.9808, what is cos$\bigl(\frac{π}{8}\bigr)$?
- 0.92
- 0.48
- 0.12
- -0.48
- -0.92
20. Simplify the expression tan$^{2}$(x) + tan$^{2}$(x) cos(2x) using the reduction formula for tangent.
- 2sinx
- 1 + cos2x
- 1 + tan2x
- 1 $-$ cos2x
- 1 $-$ sin2x
21. Using the half-angle formula, what is sin$\bigl(-\frac{π}{12}\bigl)$?
- -0.64
- -0.26
- 0
- 0.26
- 0.64
22. What is cos(3x) cos(4x)?
- cos(12x)
- sin(3x) + cos(4x)
- $\frac{1}{2}$[cos(-x) + cos(7x)]
- $\frac{1}{2}$[cos(-x) $-$ cos(7x)]
- $\frac{1}{4}$[sin(-5x) $-$ cos(12x)]
23. What is sin(6x) $-$ sin(4x)?
- -$\frac{1}{2}$sin(2x)sin(4x)
- -2cos(4x)sin(x)
- $\frac{1}{2}$cos(4x)sin(x)
- 2sin(2x)cos(4x)
- 2sin(x)cos(5x)