An angle of a right triangle has a cotangent value of 5/12. Complete the statements using the given information and the diagram
shown on the right. a = b = c =
2 answers:
The complete question in the attached figure
Part 1) find sec (theta)
we know that
sec (theta)=1/ cos (theta)
cos (theta)=adjacent side angle theta/hypotenuse
adjacent side angle theta=5
hypotenuse=13
so
cos (theta)=5/13
sec (theta)=1/(5/13)-------> sec (theta)=13/5
the answer Part 1) is
sec (theta) = 13/5
Part 2)<span>simplify sec(theta)*cos (theta)
sec (theta)=13/5
cos (theta)=5/13
so
</span>sec(theta)*cos (theta)=(13/5)*(5/13)----> 1
<span>
the answer part 2) is 1
Part 3)</span><span>simplify cot(theta)/cos(theta)
</span><span>cot (theta)=5/12
cos (theta)=5/13
so
</span>cot(theta)/cos(theta)=(5/12)/(5/13)----> 13/12
<span>
we know that
sin (theta)=opposite angle theta/hypotenuse
opposite side angle theta=12
hypotenuse=13
sin (theta)=12/13
csc (theta)=1/sin (theta)------> csc (theta)=1/(12/13)----> csc (theta)=13/12
therefore
</span>cot(theta)/cos(theta)=csc (theta)
<span>
the answer Part 3) is
csc (theta)
Part 4)</span>simplify cot(theta)*sin(theta)<span>
cot (theta)=5/12
sin (theta)=12/13
so
</span> cot(theta)*sin(theta)=(5/12)*(12/13)----> 5/13
<span>cos (theta) =5/13
therefore
</span>cot(theta)*sin(theta)=cos (theta)
<span>
the answer part 4) is
cos (theta)
</span>
Part 1) find sec (theta)
we know that
sec (theta)=1/ cos (theta)
cos (theta)=adjacent side angle theta/hypotenuse
adjacent side angle theta=5
hypotenuse=13
so
cos (theta)=5/13
sec (theta)=1/(5/13)-------> sec (theta)=13/5
the answer Part 1) is
sec (theta) = 13/5
Part 2)<span>simplify sec(theta)*cos (theta)
sec (theta)=13/5
cos (theta)=5/13
so
</span>sec(theta)*cos (theta)=(13/5)*(5/13)----> 1
<span>
the answer part 2) is 1
Part 3)</span><span>simplify cot(theta)/cos(theta)
</span><span>cot (theta)=5/12
cos (theta)=5/13
so
</span>cot(theta)/cos(theta)=(5/12)/(5/13)----> 13/12
<span>
we know that
sin (theta)=opposite angle theta/hypotenuse
opposite side angle theta=12
hypotenuse=13
sin (theta)=12/13
csc (theta)=1/sin (theta)------> csc (theta)=1/(12/13)----> csc (theta)=13/12
therefore
</span>cot(theta)/cos(theta)=csc (theta)
<span>
the answer Part 3) is
csc (theta)
Part 4)</span>simplify cot(theta)*sin(theta)<span>
cot (theta)=5/12
sin (theta)=12/13
so
</span> cot(theta)*sin(theta)=(5/12)*(12/13)----> 5/13
<span>cos (theta) =5/13
therefore
</span>cot(theta)*sin(theta)=cos (theta)
<span>
the answer part 4) is
cos (theta)
</span>
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