Question

5) Use a calculator and find to 4 decimal places the value of the trigonometric function using the given identity.

2u = 64° , cos 2u = 1 -2 sin ^2 u
a.) 0.0792

b.) 0.3327

c.) 0.9992

d.) 0.5629

e.) 0.4384

Answer 1

cos(2u) = 1 - 2
`sin^(2)`(32°) = 1 - (2
`*`0.281 ) = 1 - 0.5616 = 0.4384

Hence the correct option is E.) 0.4384

Explanation:

i) 2u = 64°

ii) u = 32°

iii) sin(32°) = 0.53

iv)
`sin^(2)`(32°) =
`(0.53)^(2)` = 0.2808

v) cos(2u) = 1 - 2
`sin^(2)`(32°) = 1 - (2
`*`0.2808 ) = 1 - 0.5616 = 0.4384

Hence the correct option is E.) 0.4384