9.10 Gradient of a line using trigonometric ratios
Write an expression for the gradient of the line that is inclined at an angle of 33\degree to the positive x-axis.
Find the gradient of a line that is inclined at an angle of 50\degree to the positive x-axis . Round your answer to one decimal place.
Find the angle of inclination of a line to the positive x-axis, whose gradient is 4. Round your answer to the nearest degree.
Consider the given line with an angle of inclination of \theta with the positive x-axis:
Find the gradient of the line.
Hence, find \theta. Round your answer to two decimal places.
Point P \left(5.2, 5.72\right) lies on the given line passing through the origin:
Find \theta, the angle of inclination of the line with the positive x-axis. Round your answer to two decimal places.
For each of the linear equations below, find \theta the angle of inclination of the line with the positive x-axis. Round your answer to the nearest degree.
Consider the graph of the line y = \dfrac{1}{2} x + 1 given and the triangle whose vertices are the origin, the x-intercept and the y-intercept. \theta is the acute angle in the triangle that the line makes with the x-axis.
State the gradient of the line.
Find the value of \tan \theta.
Point P \left(15, 7\right) lies on the given line passing through the origin:
Find \theta, the angle of inclination of the line with the positive x-axis. Round your answer to two decimal places.
A line makes an angle of \theta with the positive x-axis. If \theta \lt 90 \degree. State whether the gradient of the line is positive or negative.
If a line has a gradient of - 4 and an angle of inclination of \theta with the positive x-axis, which of the following is true of the value of \theta?
-90\degree < \theta < 0\degree
0\degree < \theta < 90\degree
90\degree < \theta < 180\degree
180\degree < \theta < 270\degree
Two points A \left(1, - 2 \right) and B \left(9, 30\right) lie on a line that makes an angle of \theta degrees with the positive x-axis.
Find the gradient of the line.
Find \theta to two decimal places.
Find \theta, the angle of inclination of the line with the positive x-axis, if the x-intercept is - 5 and the y-intercept is 9. Round your answer to two decimal places.
A line with gradient m has an angle of inclination of 65 \degree with the positive x-axis, such that \tan 65 \degree = m. Without solving for m, find the value of \theta such that \tan \theta = - \dfrac{1}{m}.
Find \theta, the angle of inclination of the line with the positive x-axis for a line with a gradient of - \dfrac{1}{\sqrt{3}}.
A horizontal line makes an angle of 0 \degree with the x-axis.
Evaluate \tan 0 \degree by considering its relationship to the gradient of the line.
A vertical line is perpendicular to a horizontal line. Using the fact that the gradients of perpendicular lines have the relationship m_{1} \times m_{2} = - 1, find the value of \tan 90 \degree.
A line is drawn on the cartesian plane at an angle of inclination \theta with the positive x-axis. Given that \sin \theta = \dfrac{12}{13}, find the gradient m of the line.
Line L_{1} makes an angle of \theta with the positive x-axis. Line L_{2} is such that it is perpendicular to line L_{1}. Form an expression for the gradient of line L_{2} in terms of \theta.
A line passing through the points \left(2, - 3 \right) and \left(x, 9\right) makes an angle of 120 \degree with the positive x-axis. Find the exact value of x.
The steepness of a ski run is defined by the angle of inclination of the run with the horizontal ground.
By how many degrees is Run A steeper than Run B? Round your answer to one decimal place.
