Question

Find the side labeled x. State your answer rounded to 5 decimal places. 510 21 21. (-12.94 Points) DETAILS SPRECALC7 6.3.047 Find the values of the trigonometric functions of from the information given sin() - in Quadrant TV COS(O) tan(6)

Answer 1

1)

In right triangle ABC,

$\small sin(51^{\circ})=\frac{perpendicular}{hypotenuse}=\frac{21}{x}$

$\small x = \frac{21}{sin(51^{\circ})}=\frac{21}{0.777146}=27.02195$

$\small \therefore x =27.02195$

B A 510 21 с

2)

$\small sin\theta =-\frac{15}{17},\textup{ }\theta \textup{ lies in quadrant IV}$

$\small \textup{In quadrant IV, }sin\theta <0\textup{ and }cos\theta >0.$

$\small cos\theta =\sqrt{1-sin^{2}\theta }$

$\small cos\theta =\sqrt{1-\left ( -\frac{15}{17} \right )^{2} }$

$\small cos\theta =\sqrt{\frac{289-225}{289} }=\sqrt{\frac{64}{289}}=\frac{8}{17}$

$\small \textup{1) }cos\theta =\frac{8}{17}$

$\small \textup{2) }tan\theta =\frac{sin\theta }{cos\theta }=\frac{-15/17}{8/17}=-\frac{15}{8}$

$\small \textup{3) }csc\theta =\frac{1}{sin\theta }=\frac{1}{-15/17}=-\frac{17}{15}$

$\small \textup{4) }sec\theta =\frac{1}{cos\theta }=\frac{1}{8/17}=\frac{17}{8}$

$\small \textup{5) }cot\theta =\frac{1}{tan\theta }=\frac{1}{-15/8}=-\frac{8}{15}$

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