2
Question
The line OA makes an angle of θ=40° with the negative X-axis as shown in the figure. Which of the following could be a measure of the angle made by OA with respect to the positive Y-axis?
The line OA makes an angle of θ=40° with the negative X-axis as shown in the figure. Which of the following could be a measure of the angle made by OA with respect to the positive Y-axis?Open in App
Solution
The correct options are
B
+130˚
C
-230˚
We can measure the angle made by OA with the positive Y-axis in two directions, anticlockwise (φ) or clockwise (ϕ).
For measuring angle in anticlockwise direction, we see
φ=(90˚+θ) =(90˚+40˚) =+130˚
Also, in clockwise direction,
angle made ϕ=−(180˚+(90˚−40˚)) =−(180˚+50˚) =−230˚
So, measuring the angle subtended in clockwise direction, we getangle ϕ = −230°.and, Measuring the angle subtended in anticlockwise direction, we getangle φ= +130°.
B
+130˚
C
-230˚
We can measure the angle made by OA with the positive Y-axis in two directions, anticlockwise (φ) or clockwise (ϕ).For measuring angle in anticlockwise direction, we see
φ=(90˚+θ) =(90˚+40˚) =+130˚
Also, in clockwise direction,
angle made ϕ=−(180˚+(90˚−40˚)) =−(180˚+50˚) =−230˚
So, measuring the angle subtended in clockwise direction, we getangle ϕ = −230°.and, Measuring the angle subtended in anticlockwise direction, we getangle φ= +130°.