If sin(theta)=-2/3, which of the following are possible?

Question

If sin(theta)=-2/3 which of the following are possible?

Check All that apply

*cos(theta)=√5/3 and tan(theta)=2/√5
*cos(theta)=-√5/3 and tan(theta)=2/√5
*sec(theta)=3/√5 and tan(theta)=-2/√5
*sec(theta)=-3/2 and tan(theta)=2/√5

I think all of them could be true...?


If the point P(-4/5,y) lies on the unit circle and P is in the third quadrant, what does y equal? If necessary, use the slash mark ( / ) for a fraction bar.?



Dr. Black is standing 15 feet from a streetlamp. The lamp is making his shadow 8 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the street lamp is 50 degrees. To the nearest foot, the streetlamp is about _____.


Which function's graph has a period of 2?
*y=2sin3x
*y=3cospix
*y=-4sin2x
*y=cos(x-pi/2)

Answer 1

sin(x)=-2/3

sin(x) is negative so sin(x) is in the 3rd or 4th quadrant

first find the missing side of the right triangle

3²=m²+2²

9=m²+4

9-4=m²

m²=5

m=√5

cos(x)=√5/3 in the 4th quadrant and tan is negative in the 4th quadrant

tan(x)=-2/√5 in the 4th quadrant

cos(x)=-√5/3 in the 3rd quadrant and tan(x)=2/√5 in the 3rd quadrant so first is false and second is true

sec(x)=1/cos=3/√5 or -3/√5 so that eliminates the fourth answer

sec(x)=3/√5 and tan(x)=-2/√5 is true because cos(x) is positive in the 4th quadrant and tan(x) is negative in the 4th quadrant and tan(x) we found to be 2/√5 in the 3rd quadrant

 

P(-4/5,y) is on the unit circle in the 3rd quadrant

x²+y²=1 is the equation of the unit circle

(-4/5)²+y²=1

y²=1-16/25

y²=9/25

y=3/5 or -3/5

in the 3rd quadrant y is negative so y=-3/5

 

tan(50º)=h/7

1.19175359=h/7

h=7*1.19175359

h=8.34 feet

h=8 feet

 

period=2(pi)/b

y=3cos(pi)x

period=2(pi)/(pi)=2