# 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

### Comments for Exact Value of Given Expression - Analythic Trig

 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