All High School Math Resources
Example Question #1 : Understanding Sine, Cosine, And Tangent
If the polar coordinates of a point are , then what are its rectangular coordinates?
The polar coordinates of a point are given as , where r represents the distance from the point to the origin, and represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)
The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.
In this problem, the polar coordinates of the point are , which means that and . We can apply the conversion formulas to find the values of x and y.
The rectangular coordinates are .
The answer is .
Example Question #2 : Trigonometry
What is the ?
Example Question #3 : Trigonometry
In the right triangle above, which of the following expressions gives the length of y?
is defined as the ratio of the adjacent side to the hypotenuse, or in this case . Solving for y gives the correct expression.
Example Question #2 : Understanding Sine, Cosine, And Tangent
What is the cosine of ?
The pattern for the side of a triangle is .
Since , we can plug in our given values.
Notice that the 's cancel out.
Example Question #3 : Understanding Sine, Cosine, And Tangent
If , what is if is between and ?
Recall that .
Therefore, we are looking for or .
Now, this has a reference angle of , but it is in the third quadrant. This means that the value will be negative. The value of is . However, given the quadrant of our angle, it will be .