From cosine to sine

Geometry Level 1

Suppose

$\cos\theta = \frac{3}{5},\quad \sin2\theta = \frac{a}{b},$

where $0<\theta <\frac{\pi}{2}$ with $a$ and $b$ coprime positive integers.

What is the value of $a+b?$

2 solutions

Anuj Raj
Oct 31, 2014

cos x= 3/5, sin2x= 2sinx*cosx sin2x= 24/25 sin2x= a/b a+b= 49

Ramasubramaniyan Gunasridharan
Apr 27, 2014

sin 2x = 2sinxcosx = 2sinx 3/5 = sinx 6/5. sqrt(1-cos^2 x) = sinx = 4/5. Thus 4/5 *6/5 =24/25. Thus, a = 24 , b =25. Thus, 24+25 =49

a/b =24/25. Hence (b+a)/(b-a) =49/1.So a+b =49

vinod trivedi - 6 years, 10 months ago