How do you solve ${sec}^{2} x + 0.5 tan x = 1$ $sec^2x+0.5tanx=1$ and find all solutions in the interval $[0, 2 π)$ $[0,2pi)$ ?

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How do you solve ${sec}^{2} x + 0.5 tan x = 1$ $sec^2x+0.5tanx=1$ and find all solutions in the interval $[0, 2 π)$ $[0,2pi)$ ?

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Answer 1 · 2016-07-10T22:26:50

$0, 153^{\circ} 43, 180^{\circ}, 333^{\circ} 43$ $0, 153^@43, 180^@, 333^@43$

Explanation:

Call tan x = t. Apply the trig identity:
$1 + t^{2} = {sec}^{2} x$ $1 + t^2 = sec^2 x$
The equation is transformed to:
$1 + t^{2} + \frac{t}{2} = 1$ $1 + t^2 + t/2 = 1$
t^2 + t/2 = 0
t(t + 1/2) = 0
There are 2 cases:
a. t = tan x = 0 --> arc x = 0 and arc x = pi
Calculator gives:
b. tan x = -1/2 --> arc $x = - 26^{\circ} 57$ $x = - 26^@57$ and $x = - 26.57 + 180 = 153^{\circ} 43$ $x = -26.57 + 180 = 153^@43$ .
The co-terminal arc of $x = - 26^{\circ} 57$ $x = -26^@57$ is: arc $x = 333^{\circ} 43$ $x = 333^@43$
Answers for $(0, 360)$ $(0, 360)$ :
$0, 153^{\circ} 43, 180^{\circ}, 333^{\circ} 43$ $0, 153^@43, 180^@, 333^@43$

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How do you solve ${sec}^{2} x + 0.5 tan x = 1$ $sec^2x+0.5tanx=1$ and find all solutions in the interval $[0, 2 π)$ $[0,2pi)$ ?

1 Answer

Explanation:

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How do you solve sec^2x+0.5tanx=1sec2x+0.5tanx=1sec^2x+0.5tanx=1 and find all solutions in the interval [0,2pi)[0,2π)[0,2pi)?

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Explanation:

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How do you solve ${sec}^{2} x + 0.5 tan x = 1$ $sec^2x+0.5tanx=1$ and find all solutions in the interval $[0, 2 π)$ $[0,2pi)$ ?