How do you solve #tan(x)=1/2#?

2 Answers
Feb 21, 2016

Answer:

#color(blue)(x = 26.565051)#

Explanation:

Since the given is a "Trigonometric Function of Tangent (Tan)",
and #x# is an angle #theta# (Theta),

#tan# #theta##=1/2#

to get the value of #x# or #theta#, we can use some algebraic techniques to isolate the variable #theta# from #tan#,

By simply transposing #tan# on both sides (Golden Rule of Algebra) - (Balancing All Sides of the Equation)

#(canceltan theta/canceltan ) = ((1/2)/tan)#
#theta = (1/2)*(1/tan)#
#theta = arctan(1/2)#

arctan #(1/tan) or tan^-1# is the inverse function of tan function,

#theta = tan^-1(1/2)#

#theta = 26.565051#

Dec 18, 2017

Answer:

#t = 26^@57 + k360^@#

Explanation:

#tan t = 1/2#
Calculator and unit circle give 2 solutions for (0, 360) -->
#t = 26^@57# , and #t = 180 + 26.57 = 206^@57#
General answer:
#t = 26^@57 + k360^@#