You should know that and , where is the radius (in your case, length of the arm).
So first evaluate using Pythagoras and your two points and , then you can evaluate and .
Do the same for Q7.
I need help understanding the following questions:
6. The point (20, 21) is on the terminal arm of an angle θ in standard position. Find sin θ and cos θ.
7. The point (-8, 6) is on the terminal arm of an angle θ in standard position. Find sin θ and cos θ.
I thought it was draw the point on the graph and then find the angle from the origin (sin 0). But the teacher said no. This is not what it means. She did not know what it meant. As well, what does it mean by sin θ and cos θ? I have no idea what it means.
I suggest you research the unit circle.
But yes, you have been given enough information to create a right-angle triangle, and you don't need to know anything about the angles.
Draw a set of Cartesian axes and join the origin to the point (20, 21).
Surely you can see that the angle made with the positive x axis (which you don't need to measure) gives the opposite side = 21 units and the adjacent side = 20 units.
Use Pythagoras to find the length of the Hypotenuse and you can find and .
I wanted to label the angles differently as I placed both on a single diagram.
The is the second angle formed by (0, 0) and (-8, 6)
If we subtract from then we get your second which starts from the positive side of the x-axis anticlockwise,
as does the first
From the sketch, you can work with the acute angle shown in the green triangle.
One of the angles that you want is greater than 90 degrees,
so the title refers to that one.
When calculating Sine and Cosine of angles greater than 90 degrees,
we use the horizontal and vertical co-ordinates,
horizontal for Cosine, which is why the numerator has
for your larger angle,
vertical for Sine, which is why the numerator has for the second angle.
When the angles are less than 90 degrees, working with the side lengths
of a right-angled triangle suffices.