How do you use a calculator to evaluate #cos^-1 0.24# in both radians and degree?

2 Answers
Maksymilian M.
Jun 2, 2018

76.113#@# and/or #(76133pi)/180000#

Explanation:

First i would get the degree by doing #cos^-1(0.24)# in a calculator to get 76.113#@#
This is #76.133# out of #360# which is #76.133/360#
Radians is out of #tau# or #2pi# To find out radian multiply the fraction by #tau# or #2pi# to get:
#76.133/360*2pi=(152.266pi)/360=(76133pi)/180000#

Nghi N.
Jun 3, 2018

#x = 76^@, or (19pi)/45#
#x = 284^@, or (71pi)/45#

Explanation:

#cos ^-1 (0.24)# --> arccos (0.24)
Calculator and unit circle give -->
cos x = 0.24 -->
arc #x = +- 76^@#
For #(0, 360^@)# the answers are:
#x = 76^@# and
#x = 284^@# (co-terminal to #-76^@#)
Convert to radians:
#x = 76^@# --> #x = (76 pi)/180 = (19pi)/45#.
#x = 284^@# --> #x = (284pi)/180 = (71pi)/45#

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