How to find negative sine - ACT Math
Card 0 of 4
If 
, what is 
if 
is between 
and 
?
If
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 
.
Recall that
Therefore, we are looking for
Now, this has a reference angle of
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If 
, what is the value of 
if 
?
If
Recall that the 
triangle appears as follows in radians:
Now, the sine of 
is 
. However, if you rationalize the denominator, you get:
Since 
, we know that 
must be represent an angle in the third quadrant (where the sine function is negative). Adding its reference angle to 
, we get:
Therefore, we know that:
, meaning that 
Recall that the
Now, the sine of
Since
Therefore, we know that:
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What is the sine of the angle formed between the origin and the point 
if that angle is formed with one side of the angle beginning on the 
-axis and then rotating counter-clockwise to 
?
What is the sine of the angle formed between the origin and the point
You can begin by imagining a little triangle in the fourth quadrant to find your reference angle. It would look like this:
Now, to find the sine of that angle, you will need to find the hypotenuse of the triangle. Using the Pythagorean Theorem, 
, where 
and 
are leg lengths and 
is the length of the hypotenuse, the hypotenuse is 
, or, for our data:
The sine of an angle is:
For our data, this is:
Since this is in the fourth quadrant, it is negative, because sine is negative in that quadrant.
You can begin by imagining a little triangle in the fourth quadrant to find your reference angle. It would look like this:
Now, to find the sine of that angle, you will need to find the hypotenuse of the triangle. Using the Pythagorean Theorem,
The sine of an angle is:
For our data, this is:
Since this is in the fourth quadrant, it is negative, because sine is negative in that quadrant.
Compare your answer with the correct one above
What is the sine of the angle formed between the origin and the point 
if that angle is formed with one side of the angle beginning on the 
-axis and then rotating counter-clockwise to 
?
What is the sine of the angle formed between the origin and the point
You can begin by imagining a little triangle in the third quadrant to find your reference angle. It would look like this:
Now, to find the sine of that angle, you will need to find the hypotenuse of the triangle. Using the Pythagorean Theorem, , where and are leg lengths and is the length of the hypotenuse, the hypotenuse is , or, for our data:
The sine of an angle is:
For our data, this is:
Since this is in the third quadrant, it is negative, because sine is negative in that quadrant.
You can begin by imagining a little triangle in the third quadrant to find your reference angle. It would look like this:
Now, to find the sine of that angle, you will need to find the hypotenuse of the triangle. Using the Pythagorean Theorem,
The sine of an angle is:
For our data, this is:
Since this is in the third quadrant, it is negative, because sine is negative in that quadrant.
Compare your answer with the correct one above