The point (- 1/3, 1/2) is a point on the terminal side of angle theta in standard position. Find the
exact values of the six trigonometric functions of angle theta Find all values of x for which each
of the following is undefined. (a) f(x) = tan(3x) (b) g(x) = csc x (c) q(x) = sin(5x) (d) P(x) =
sec(2x + 3) Given that sin theta = -0.75, find 7 sin(theta + 2 pi) - 3 sin(theta + 8 pi) + 6 sin(theta
- 10 pi) Given that theta is in quadrant II and tan theta = -8/7, find cos theta Sketch the graph of
each of the following: (a) f(x) = sin x (b) g(x) = cos x (c) q(x) = tan x (d) P(x) = cot x (e) W(x)
= sec x (f) R(x) = csc x
Solution
8. (-1/3,1/2)
Tan theta=y/x=-3/2
Opposite=3 adjacent=2
Hypotenuse=sqrt13
Sin theta=opposite/hypotenuse=-3/sqrt13
Cos theta=adjacent/hypotenuse=2/swrt13
Csc theta=1/sin theta=-sqrt13/3
Sec theta=1/cos theta=sqrt13/2
Cot theta=1/tan theta=-2/3.
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The population of a city is 7 million, with exponential growth rate .pdf
1. The population of a city is 7 million, with exponential growth rate 4%. In how many years will
the population double in size?
Solution
genral exponential growth equation is P(t)=(P(0))ert
here population P(t) is in millions
The population of a city is 7 million =>P(0)=7
exponential growth rate 4% => r =4/100=0.04
population double =>P(t)=2*7=14 million
P(t)=(P(0))ert
=>14=7*e0.04t
=>e0.04t =(14/7)
=>e0.04t =2
=>0.04t =ln(2)
=>t=(1/0.04)ln(2)
=>t=17.33 years
so population doubles in size in 17.33 years approximately
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