0 like 0 dislike
23 views
If $\tan \theta=\frac{3}{4}$ and $\theta \in\left(180^{\circ} ; 360^{\circ}\right)$ calculate without the use of a calculator and with the aid of a diagram the value of:

(a) $\sin 2 \theta$
(b) $\cos 2 \theta$
(c) $\tan 2 \theta$
| 23 views

0 like 0 dislike
(a) $\sin 2 \theta=2 \sin \theta \cdot \cos \theta$
$\therefore \sin 2 \theta=2 \cdot\left(\frac{-3}{5}\right)\left(\frac{-4}{5}\right)$
$\therefore \sin 2 \theta=\frac{24}{25}$

(b) $\cos 2 \theta=2 \cos ^2 \theta-1$
\begin{aligned} & \therefore \cos 2 \theta=2\left(\frac{-4}{5}\right)^2-1 \\ & =\frac{32}{25}-1=\frac{7}{25} \end{aligned}

(c) $\tan 2 \theta=\dfrac{\sin 2 \theta}{\cos 2 \theta}$
$\therefore \tan 2 \theta=\dfrac{\dfrac{24}{25}}{\dfrac{7}{25}}=\dfrac{24}{7}$
by Diamond (75,025 points)

0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
1 like 0 dislike
1 like 0 dislike
1 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike