Precalc Chapter 6 formulas

Given the following triangle, which formula would you use to find angle A?

• $\frac{7}{\sin35}=\frac{a}{\sin\ 105}$

• $\frac{\sin105}{c}\ =\ \frac{\sin35}{7}$

• $A\ =\ \sin^{-1}\left(\frac{7\sin35}{\sin\ 105}\right)$

• $180\ -\ \left(35\ +\ 105\right)$

Write the formula for finding angle R

• $\arcsin(28\sin39/41)$

• $\frac{28}{\sin39}\ =\ \frac{41}{\sin\ R}$

• $28^2\ +\ 41^{2\ }-2\left(28\right)\left(41\right)\cos39\degree$

• $\frac{1}{2}\left(28\right)\left(41\right)Sin39\degree$

Write the formula for finding side c

Which is not a valid Law of Cosine formula?

• $b\ =\ \sqrt{\left(a^2\ +c^2-2ac\ CosB\right)}$

• $\frac{\cos A}{a}=\frac{\cos B}{b}$

• $\cos\ C=\frac{\left(b^{2\ }+a^2\ -\ c^2\right)}{2\left(a\right)\left(b\right)}\$

• $a^2=b^2+c^2\ -2bc\ CosA$

What formula would you use for finding the area of this triangle?

• You need to first find the side p or angle P before finding the area.

• You can't find the area of this triangle with the information given

 $v\ =<v_1,\ v_2>\ and\ w\ =\ <w_1,\ w_2>$  

What is  $v\cdot w$  ?

•  $v_1w_1+v_2w_2$  

•  $<v_1w_{1\ ,}\ v_2w_2>$  

•  $<v_1+w_1\ ,\ v_2+w_2>$  

•  $v_1w_1\ i\ +\ v_2w_2\ j$  

Given $\parallel v\parallel\ =\ 52\ and\ \theta\ =\ 63$  find the linear combination for vector v.

•  $52\ i\ +\ 63j$  

•  $52\cos63i\ +52\ \sin\ 63j$  

•  $63\ \cos52\ +\ 63\ \sin52$  

•  $\frac{\cos63}{52}\ i+\frac{\sin63}{52}j\$  

Find the component form of vector starting at (3 , -8) and terminating at (2, -7)

• <5 , -15>

• <1, -1>

• < -1, 1>

• < 6, 56>

Which formula works to find the angle  $\theta$  between two vectors

•  $\left(v+w\right)\cos\theta\ i\ +\left(v+w\right)\sin\theta\ j$  

•  $\tan^{-1}\left(v+w\right)$  

•  $\cos^{-1}\left(\frac{\left(v\cdot w\right)}{\parallel v\parallel\parallel w\parallel}\right)$  

•  $\tan\ \theta_v\ +\ \tan\theta_w$  

What Quadrant would the resultant vector be found in if

v = -132 i + 45 j and w = 83 i + 33 j

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV