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Exact Value of Given Expression - Analythic Trig

by Zachary
(CA, USA)












































Find the exact value of the given expression.

Cos(2 tan⁻¹(15/8))

1. find the arc tangent of 15/8

2. find the cos of 2 x this value

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May 04, 2012
Exact Value of Given Expression - Q7.123
by: Staff


Question:


by Zachary
(Campbell CA, USA)

Find the exact value of the given expression.


Answer:


For a right triangle

tan Θ = (opposite side/adjacent side)

tan Θ = (15/8)


The inverse tangent (or arc tangent) refers to the angle Θ rather than the value of the tangent (which is 15/8). In other words, you begin with a known tangent and calculate the angle, rather than the other way around.

Θ = tan⁻¹(15/8)

Θ = tan⁻¹(1.875)

You can use a calculator or a table to calculate Θ

Θ = 1.0808390005412 radians

1 rad = 57.296... deg.

Θ = 61.9°


--------------------------

Cos[2 tan⁻¹(15/8)]

= Cos[2 * 61.9°]

= Cos[123.8°]

Or

= Cos[2 * 1.080839 rad]

= Cos[2.161678 rad]

= Cos[2.161678 rad]

= -0.5570934256055



>>> the final answer is:

Cos[2 tan⁻¹(15/8)] = -0.5570934256055





Thanks for writing.

Staff
www.solving-math-problems.com



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