\( \sin t=\frac{5}{13}, \quad 0<t<\frac{\pi}{2} \) бол \( \operatorname{tg} t=? \)

1.7 Determine the value of \( \theta \), if \( \theta \in\left[0^{\circ} ; 90^{\circ}\right] \), correct to 3 decimal places : 1.7.1 \( 3 \cos \theta=1,203 \) \( 1.7 .2 \quad 5 \cos x+2=4 \) \( 1.7 .3 \quad \frac{4}{3} \sin \theta=\cos 37^{\circ} \) \( 1.7 .4 \quad \tan 3 \theta=6,345 \) \( 1.7 .5 \quad \frac{\tan \theta}{2}=2,5 \) \( 1.7 .6 \quad 2 \sin \left(\theta+15^{\circ}\right)=1,462 \)

Minimum value is \( 13 \times(-1)=-13 \) \( A+B=45^{\circ} \), Prove that \( (1+\tan A)(1+\tan B)=2 \)

1.5 It is known that \( 13 \sin \alpha-5=0 \) and \( \tan \beta=-\frac{3}{4} \quad \) where \( \alpha \epsilon\left[90^{\circ} ; 270^{\circ}\right] \) and \( \beta \epsilon\left[90^{\circ} ; 270^{\circ}\right] \). Determine, without using a calculator, the value of the following: \( 1.5 .1 \cos \alpha \)

7. \( \frac{2 \cos x-5 \sin x}{3 \sin x-4 \cos x}=\frac{2}{3} \) ise \( \tan x \) in değeri kaçtır?

In terms of the sides of a right triangle, how would you express \( \tan(\theta) \)?