If the sine of theta is (3/8) and theta is in the first quadrant, what is sin 2(theta)?
a.) (3(sqrt55))/32
b.) (sqrt55)/8
c.) (2sqrt55)/32
d.) 3/8

Question

If the sine of theta is  (3/8) and theta is in the first quadrant, what is  sin 2(theta)? 
a.) (3(sqrt55))/32
b.) (sqrt55)/8
c.) (2sqrt55)/32
d.) 3/8

campbell_st · Answer

1st draw a triangle and find the missing side using pythagoras

|dw:1348710222551:dw|

then you can use the double angle expansion of sin(2x)

$$\sin(2\theta) = 2 \sin(\theta)\cos(\theta)$$

anonymous · Answer

so the answer would be c? (2sqrt55)/32?

campbell_st · Answer

its 

$$2 \times \frac{3}{8} \times \frac{\sqrt{55}}{8}$$