PLS HELP WITH THIS!!!!!
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In these questions, we need to follow the steps:
1 - solve for the trigonometric function
2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.
3 - Complete these angles with the complete round repetition, by adding
4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for <em>x</em> to get the solutions.
1 - To solve, we just use algebraic operations:
2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:
The value for the angle that give positive
is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of
Are:
3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:
Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:
4 - Now, we need to solve for <em>x</em>, because these solutions are for all the interior of the tangent function, so:
So, the solutions are:
y = - x +
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = 4x + 5 is in this form with slope m - 4
Given the slope of a line m, then the slope () of a line perpendicular to it is
= - (1 / m ) = -
y = - x + c is the partial equation of the perpendicular line
to find c, substitute ( 2, 7 ) into the partial equation
7 = - + c ⇒ c =
y = - x +
← equation of perp. line