Math 127 - Fall 2022
Practice Quiz 3
Multiple Choice: Select the best answer(s) out of the options.
1. Select all true statements:
1 7 thenx= 6 arcsin x (b) = arctan x arccos x (c) arcsin(2 cos x sin x)=2x TT
2. What is the period of sin 2x + sin 4x?
(a) T (b) 2 T (c) 2T
3. Select the true statement(s)
(a) If f and g are invertible functions both having range and domain equal to R, then (f o g)-1 exists and (f o g)-1 =(f-1 o g-1) (b) If both f and g are even and both f o g and g o f exist, then f o g and g o f are both even. (c) If both f and g are odd and both f o g and g o f exist, then f o g and g o f are both odd. (d) If f is odd and invertible then f-1 is even. (e) If f is odd and invertible then f-1(0) = 0.
4. Suppose that a person takes a breath 15 times per minute on average (one breath is an inhale and exhale) Each exhale expels 500 mL of air from the lungs and each inhale brings in 500 mL of air. Assuming that there is always a reserve of at least 1L of air, which of the following best models the volume of a pair of lungs (in litres) as a function of time (in seconds)?
aVt)=
A
2
(c) V(t)= sin (2T -
+
5. Which of the following is equal to tan arcsir
(a) 3 (b) 2 (c) 3 (d) 2 (e) v5 (f) s5
6. Which of the following is equal to sin (arccos
5 (a) 3 3 (b) 3 (c)5 (a) 7. What is the value of cos (G
1
(b) (1 + V3) 2/2
(c) (1 - V3) 2/2 (d) (V3 - 1) 2V2
8. (i) If someone who stands 150 cm tall sees the sun at an angle of 3 above the horizon, how long is their shadow? (a) 75 cm (b) 150 cm w (e) (d) 150V2 cm (ii) Suppose that on that day, the angle of the sun with respect to the horizon is given by 0(t) =
(i) of this question measured their shadow to be 150 cm long, what time is it?
(a) 10 a.m. (b) 9 a.m. (c) 5 p.m. (d) Either (b) or (c) (e) Either (a) or (c)
2
9. Which of the following points do not lie on the unit circle?
(a)(12) (b) (1,0)
(c)
V5 2v29 (d) 11 11
/3 1 (e)
10. Which of the following are true?
(a) -xx<|x|for all xeR (b) The solution to |x|< 2 is x E (-,2) (c) If|x|> a for some a E R then x > a. (d) |x+y|=|x|+|y|for all x,y E R. (e)[xy|=[x|y|for all x,yE R.
11. Which of the following are false?
(a) cos(x)=cos(x+2T)
(b) tan(x)=tan(x+T)
(c) arcsin(x) = sin x