### All Trigonometry Resources

## Example Questions

### Example Question #11 : Unit Circle And Radians

Suppose there is exists an angle, such that .

For what values of and make this trigonometric ratio possible?

**Possible Answers:**

**Correct answer:**

The only values such that

are at the values:

This means that the only choice for is . or achieve the necessary angles to satisfy this trigonometric ratio.

### Example Question #12 : Unit Circle And Radians

If , and , what is ?

**Possible Answers:**

**Correct answer:**

The tangent of an angle yields the ratio of the opposite side to the adjacent side.

If this ratio is , we can see that this is a Pythagorean triple (3-4-5); the absolute value of the sine of this angle would be .

However, the question indicates that this angle lies in the 3rd quadrant. The sine of any angle in the 3rd or 4th quadrant is negative, since it is equivalent to the *y*-coordinate of the corresponding point on the unit circle.

Therefore,

.

### Example Question #13 : Unit Circle And Radians

If , which of the following angles is **NOT **a possible value for ?

**Possible Answers:**

**Correct answer:**

On the unit circle, the cosine of an angle yields the *x*-coordinate.

There are two angles at which the *x-*coordinate on the unit circle is : and .

is coterminal with , and is coterminal with .

is in the 4th quadrant, and has a positive *x*-coordinate.

### Example Question #361 : Trigonometry

How many degrees are in a unit circle?

**Possible Answers:**

**Correct answer:**

Step 1: Define a Unit Circle:

A unit circle is used in Trigonometry to draw and describe distinct angles. The unit circle works along with the coordinate grid.

Step 2: There are quadrants in the coordinate grid, each quadrant can fit degrees.

Step 3: Multiply how many degrees in quadrant by .. to get the full unit circle:

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