Trigonometry : Unit Circle

Study concepts, example questions & explanations for Trigonometry

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Example Questions

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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:

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

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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