High School Math : Understanding Sine, Cosine, and Tangent

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Understanding Sine, Cosine, And Tangent

If the polar coordinates of a point are , then what are its rectangular coordinates?

Possible Answers:

Correct answer:

Explanation:

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

Triangle

What is the ?

Possible Answers:

 

Correct answer:

Explanation:

 

Example Question #3 : Trigonometry

Triangle

In the right triangle above, which of the following expressions gives the length of y?

Possible Answers:

Correct answer:

Explanation:

 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 ?

Possible Answers:

Correct answer:

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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 .

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