1)FACTOR AND SOLVE TO TWO DECIMAL PLACES: 2sin^2x+sinx=0 DOMAIN 0_<x_<2pi 2)Prov

Question

1)FACTOR AND SOLVE TO TWO DECIMAL PLACES:

2sin^2x+sinx=0 DOMAIN 0_<x_<2pi

2)Prove the isentity:

tantheta-1=sin^2theta-cos^2theta/sinthetacostheta+cos^2theta

3)WRITE the equation of a curve in the FORM y=asin k(x+c) +d that has the following characteristics: an amplitude of 5, a period of 720degrees, a phase shift of 45 degrees to the right and a range -3_<y_<7.

4)The height of pedal of a bicycle varies as the bike moves.h=15sin(4pi)t+23.Time has been measured in seconds.

a)What is the pedal's maximum height above the ground?

b)How long does it take for the pedal to complete one revolution?

c)When is the pedal at a height of 8cm?

5)The population of an information technology village is increasing by 8% per year. In 2004, there were 4500 people living in the village.

a)Estimate the popluation in 2010.

b)The half-life of radium is 1620 years.

i)If a laboratory initially had 5 g of radium, determine how much they would have in 200 years?

ii)How many years would it take until the laboratory had only 4 g of radium?

Calculus

Explanation / Answer

Here 2sin^2x+sinx=0

so we get sinx(2sinx+1)=0

Hence sinx = 0 or sinx = -1/2

so x will be 0 or 210 or 330 degrees

there will be three possibilities.

2.

tan(theta)-1=[sin^2theta-cos^2theta]/[sintheta*costheta+cos^2theta].........to prove

[sin^2theta-cos^2theta]/[sintheta*costheta+cos^2theta] consider theta as x

[sin^2x-cos^2x]/[sinx*cosx+cos^2x]

= (sinx+cosx)*(sinx+cosx)/{[sinx+cosx]*cosx}

=cancelling gives sinx+cosx/cosx = tanx+1

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