Simplifying a Trigonometric Expression In Exercises \(33 - 40\) , use the fundamental identities to simplify the expression. (There is more than one correct form of each answer.) 33. \(\tan \theta \csc \theta\)
35. \(\sin \phi ( \csc \phi - \sin \phi )\)
37. \(\sin \beta \tan \beta + \cos \beta\)
39. \(\frac { 1 - \sin ^ { 2 } x } { \csc ^ { 2 } x - 1 }\)
Simplify \( \sin ( x ) ( \csc ( x ) - \sin ( x ) ) : \cos ^ { 2 } ( x ) \)
Steps
\( \sin ( x ) ( \csc ( x ) - \sin ( x ) ) \)
Express with sin, cos
\( = 1 - \sin ^ { 2 } ( x ) \)
Rewrite using trig identities
\( = \cos ^ { 2 } ( x )\)
Find the distance between each pair of points. Round your answer to the nearest tenth. \(( - 0.6,7.1 ) , ( 6.8,5.6 )\)
A) \(3\) B) \(7.6\) C) \(14.1\) D) \(11.1\) 10) \(( 1.3,4.9 ) , ( - 1 , - 3.3 )\)
A) \(8.5\) B) \(3.2\) C) \(2.4\) D) \(1.6\)
17. A ladder leaning against a wall makes an angle of \( 75 ^ { \circ } \) with the ground. If the foot of the ladder is \( 6 \) feet from the base of the wall, what is the length of the ladder?
