If and, in the ambiguous case, , , and are given, and are the two values of . If is…

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

\angle A=45^\circ

and, in the ambiguous case,

a

b

, and

A

are given,

c_1

and

c_2

are the two values of

c

. If

\theta

is the angle between the two positions of the ambiguous side

c

, then

\cos\theta

is: (1)

\frac{c_1c_2}{c_1^2+c_2^2}

(2)

\frac{2c_1c_2}{c_1^2+c_2^2}

(3)

\frac{\sqrt{c_1c_2}}{c_1+c_2}

(4)

\frac{2\sqrt{c_1c_2}}{c_1+c_2}