How do you calculate \tan(\arccos(\frac{5}{13})) ?

blitzbabeiy 2022-01-21 Answered
How do you calculate tan(arccos(513)) ?
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Expert Answer

Amina Hall
Answered 2022-01-22 Author has 11 answers
If you set α=arccos(513)cosα=513 than we have to calculate:
tanα=sinαcosα
cosα=513sinα=1cos2α=125169
=16925169=144169=1213
So:
tanα=1213513=1213135=125
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Aaron Hughes
Answered 2022-01-23 Author has 13 answers
tan(arccos(513))
Draw a triangle in the plane with vertices (513,12(513)2),(513,0), and the origin. Then (513) is the angle between the positive x-axis and the ray beginning at the origin and passing through (513,12(513)2). Therefore, tan(arccos(513)) is 12(513)2513.
Multiply the numerator by the reciprocal of the denominator.
12(513)2135
One to any power is one.
1(513)2135
Apply the product rule to 513
Raise 5 to the power of 2.
125132135
Raise 13 to the power of 2.
125169135
Write 1 as a fraction with a common denomiantor.
16916925169135
Combine the numerators over the common denominator.
16925169135
Subtract 25 from 169.
144169135
Rewrite 144169 as 144169.
144169135
Simplify the numerator.
12169135
Simplify the denomiantor.
1213135
Simplify terms.
125
The result can be shown in multiple forms.
Exact Form:
125
Decimal Form:
2.4
Mixed Number Form: 225
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