Question

Find sin2a, cos2a, and tan2a if tana=-sqrt3, and pi/2 11 years ago

Answer 1

well you know the angle is in the 2nd quadrant...

so draw a diagram and use pythagoras' theorem



then use the expansions

sin(2a) = 2 sin(a)cos(a)

cos(2a) = cos^(a) - sin^2(a)

etc...

Answer 2

could I just say the hypotenuse is 2? 30-60-90 triangle

Answer 3

@campbell_st

Answer 4

that's correct.... the hypotenuse is 2...

so now you can find

sin(a) and cos(a)

and then answer your questions...

be careful with the signs of the terms... in the 2nd quadrant only sin is positive,.

Answer 5

sin2a=2sinAcosA right?

Answer 6

that's correct but be careful cos(A) is negative...

Answer 7

so \[(\frac{ \sqrt{3} }{ 2 })(2)(-\frac{ 1 }{ 2 })=-\frac{ \sqrt{3} }{ 2 }\]

Answer 8

but isnt sin positive?

Answer 9

sin is positive... and cos is negative... so multiplying a positive by a negative gives a negative

Answer 10

okay, so is my answer correct?

Answer 11

@campbell_st

Answer 12

yes... its fine.... because when you think about doubling the size of the angle

A to 2A it puts it in the 4th quadrant where sin is negative...