Math  /  Trigonometry

QuestionPart A - Multiple Choice [K/U - 15 marks]
1. Determine the exact value of cscπ4\csc \frac{\pi}{4}. a. 12\frac{1}{\sqrt{2}} b. 2\sqrt{2} c. 32\quad \frac{\sqrt{3}}{2} d. 12\quad \frac{1}{2}
2. Determine the exact value of sin7π6\sin \frac{7 \pi}{6}. a. 2\quad-2 b. 32-\frac{\sqrt{3}}{2} c. 32\frac{\sqrt{3}}{2} d. 12-\frac{1}{2}
3. Determine the exact value of sec3π2\sec \frac{3 \pi}{2}. a. 0\quad 0 a. 0\quad 0 \qquad b. b. 1 c. -1 1 \qquad
4. An equivalent trigonometric expression for tan(π2x)\tan \left(\frac{\pi}{2}-x\right) is \qquad d. undefined \qquad a. cotx\cot x b. cotx-\cot x c. tanx\quad \tan x d. none of the above
5. Which compound angle expression is equivalent to cosxcosy+sinxsiny\cos x \cos y+\sin x \sin y ? a. sin(x+y)\quad \sin (x+y) b. sin(xy)\quad \sin (x-y) c. cos(x+y)\cos (x+y) d. cos(xy)\cos (x-y)
6. Using the subtraction formulas for sine and cosine, the compound angle formula for tan(xy)\tan (x-y) is a. tanx+tany1tanxtany\frac{\tan x+\tan y}{1-\tan x \tan y} b. tanxtany1+tanxtany\frac{\tan x-\tan y}{1+\tan x \tan y} c. tanx+tany1+tanxtany\frac{\tan x+\tan y}{1+\tan x \tan y} d. tanxtany1tanxtany\frac{\tan x-\tan y}{1-\tan x \tan y}
7. Which graph of the following functions does not have vertical asymptotes? a. y=cotxy=\cot x b. y=tanxy=\tan x c. y=sinxy=\sin x d. y=secxy=\sec x
8. The amplitude of the function y=sinxy=\sin x is a. 2π2 \pi b. π\pi c. 1\quad 1 d. 2
9. The graph of y=1y=1 intersects the graph of y=tanxy=\tan x at a. π2\quad \frac{\pi}{2} b. π4\quad \frac{\pi}{4} c. π3\frac{\pi}{3} d. π\pi
10. Determine the amplitude of the sinusoidal function y=3sin[2(xπ3)]+1y=-3 \sin \left[2\left(x-\frac{\pi}{3}\right)\right]+1. a. 2 b. -3 c. 3 d. π3\frac{\pi}{3}
11. Determine the phase shift of the sinusoidal function y=3sin[2(xπ3)]+1y=-3 \sin \left[2\left(x-\frac{\pi}{3}\right)\right]+1. a. 2 rad to the right b. 2 rad to the left c. π3rad\frac{\pi}{3} \mathrm{rad} to the left d. π3\frac{\pi}{3} to the right

Studdy Solution
1. b, 2. d, 3. d, 4. a, 5. d, 6. b, 7. c, 8. c, 9. b, 10. c, 11. d.

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord