Answer:
see below
Step-by-step explanation:
As sin(t) = -3 / 5 and in quadrant 4
so cos is positive
a) sin^2(t) + cos^2(t) = 1
(-3/5)^2 + cos^2(t) = 1
cos^2(t) = 1 - (9/25)
cos^2(t) = (25 - 9) / 25 = 16/25
cos(t) = +4/5
b) sin(2t) = 2 sin(t)cos(t)
= 2 * (-3/5) * (4/5)
= -24/25
c) cos(2t) = cos^(t) - sin^2(t)
= (4/5)^2 - (-3/5)^2
= 16/25 - 9 / 25
= 7 / 25
d) tan(2t) = sin(2t) / cos(2t)
= (-24/25) / (7/25)
= -24/7
e) as sin(2t) is negative and cos(2t) is positive
2t is in Quadrant 4
I am not sure for below three
f) cos(t) = cos^2(1/2 t) - sin^2(1/2 t) = 4/5
cos^2(1/2 t) + sin^2(1/2 t) = 1
by adding and solving
1 + 4/5 = 2 * cos^2(1/2 t)
9/10 = cos^2(1/2 t)
cos(1/2 t) = +- 3/[tex]\sqrt{10}[/tex]
and sin(t) = 2 * sin(1/2 t) * cos(1/2 t) = -3/5
2 * sin(1/2 t) * 3/sqrt{10} = -3/5
sin(1/2 t) = +- 1/sqrt{10}
means here sin and cos for 1/2 t should be opposite signs
so it is either 2nd or 4th quadrant
g) sin( 1/2 t) = +-1/sqrt{10}
h) cos(1/2 t) = +- 3/sqrt{10}
