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Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter (A,B,C,D, or E) in each blank. tan(arcsin(1/5 x)) cos(arcsin(1/5 x)) 1/2 sin(2 arcsin(1/5 x)) sin(arctan(1/5 x)) cos(arctan(1/5 x)) x/25 + x 2 x/25 + x 2 x/25 - x 2 x/25 25 - x 2 25 - x 2/5

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Answer:

Match each of the trigonometric expressions below with theequivalent non-trigonometric function from the following list.Enter the appropiate letter(A,B, C, D or E)in each blank

A . tan(arcsin(x/8))

B . cos (arsin (x/8))

C. (1/2)sin (2arcsin (x/8))

D . sin ( arctan (x/8))

E. cos (arctan (x/8))

These are the spaces to fill out :

.. ..........x/64 (sqrt(64-x^2))

.............x/sqrt(64+x^2)

.............sqrt(64-x^2)/8

..............x/sqrt(64-x^2)

..............8/sqrt(64+x^2)

A. ........tan(arcsin(x/8))  =......x/sqrt(64-x^2)

B .      cos (arsin (x/8))  ....sqrt(64-x^2)/8

Step-by-step explanation:

To solve this we have to find the missing sides to each of the triange discribed in prenthesis thus

A we have the sides of the triangle given by x, 8 and  [tex]\sqrt{8^{2} - x^{2} }[/tex]or  [tex]\sqrt{64 - x^{2} }[/tex]

thus tan(arcsin(x/8))  = [tex]\frac{x}{\sqrt{64 - x^{2} }}[/tex]  =

Therefore  ........tan(arcsin(x/8))  =......x/sqrt(64-x^2)

B

Here we have cos = adjacent/hypotenuse where adjacent side is [tex]\sqrt{64 - x^{2} }[/tex] and hypothenuse = 8 we have [tex]\sqrt{64 - x^{2} }[/tex]/8

B .      cos (arsin (x/8))  ....sqrt(64-x^2)/8

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