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

when sine is negative, the angle is in either the 3rd or 4th quadrant, which means cosine can be negative or positive. cos(theta) = + or - sqr5/3. secant is the inverse of the cosine, so it's also + or - 3/sqr5

tangent also is + or - 2/sqr5

If (-4/5,y) is on a unit circle, y could be any real number except 0

If the angle had been 45 degrees, the height of the lamp post would be 15+8=23 feet. Since 50>45

the lamp post is higher than 23 feet. the tan(50)=1.1975

23 x tan50 = 27.41 feet

y=3cospix has period = 2

the period = 2pi/x's coefficient = 2pi/pi= 2

3 is the amplitude