+0

# Solve for all values of x in given intervals (in radians)

+1
479
3
+79

Not sure how to do these.. Would be grateful if steps are shown and x values are in radians..

Nov 23, 2017

#1
+95884
+2

8 tan (x)  + 11  = 19     subtract 11 from  both sides

8 tan (x)  =  8      divide both sides by  8

tan ( x)  = 1

And this is true when x  =  pi/4     and   x  = 5pi/4   in  the requested interval

Nov 23, 2017
#2
+95884
+2

sec^2 (x)  = 2 tan^2 (x)

Note that   tan^2(x)  + 1  =  sec^2 (x)....so we can write

tan^2(x)  +  1  =  2tan^2(x)      rearrange as

tan^2(x)  = 1   subtract 1 from both sides

tan^2 (x)  - 1  =  0     factor

(tan (x) + 1) ( tan (x)  - 1)  = 0

Set each factor to ) and solve

tan (x)  +  1  =  0                                       tan (x) - 1  = 0

tan (x)  = -1                                               tan (x)  =  1

And this is true at                                     And this is true at

3pi/4  ± n*pi                                             pi/4  ± n*pi

Where n is an integer

Nov 23, 2017
edited by CPhill  Nov 23, 2017
edited by CPhill  Nov 23, 2017
#3
+95884
+1

sec^2(x)  + sec^2(x)  - 1  = 3    subtract 1 from both sides

2sec^2(x)  = 2     divide both sides by 2

sec^2(x)   = 1   subtract 1 from both sides

sec^2(x)  - 1  = 0     factor

( sec (x)  - 1)  (sec (x)  + 1 )   = 0

Set  each factor to 0  and solve

sec(x)  - 1  = 0                              sec(x)  +  1  = 0

sec(x)  = 1                                    sec(x)  = -1

And this is true at                        And this is true at

0  ± n*2pi                                       pi ± n*2pi

Where n is an integer

Nov 23, 2017
edited by CPhill  Nov 23, 2017