Question

If cos^2(t) < 3/4 then sin^2(t) is

a. =>0 but < 1/4

b. >1/4 but <= 1

c. >1

d. non e of the above

Answer 1

$$
cos^2(t) \lt \cfrac{3}{4}
\implies
cos(t) \lt \sqrt{\cfrac{3}{4}}
\implies
cos(t) \lt \cfrac{\sqrt{3}}{2} \implies \cfrac{adj}{hyp}\\
b = \sqrt{hyp^2-adj^2} \implies \sqrt{4-3} = 1\\
-\cfrac{1}{2} \lt sin(t) \lt \cfrac{1}{2} \implies
-\cfrac{1}{2} \lt sin^2(t) \lt \cfrac{1}{4}
$$