How to find positive cosine - ACT Math
Card 0 of 5
The value of a cosine is positive in which quadrants?
The value of a cosine is positive in which quadrants?
The cosine is positive in the 1st and 4th quadrants and negative in 2nd and 3rd
The cosine is positive in the 1st and 4th quadrants and negative in 2nd and 3rd
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Which of the following is equal to 
?
Which of the following is equal to
Here, we use the SOHCAHTOA ratios and the fact that csc x = 1 / sin x.
Cosine x = adjacent side length / hypotenuse length
Cosecant x = 1 / sin x = hypotenuse / opposite
(Adjacent / hypotenuse) * (hypotenuse / opposite) = Adjacent / opposite = Cotangent x.
Here, we use the SOHCAHTOA ratios and the fact that csc x = 1 / sin x.
Cosine x = adjacent side length / hypotenuse length
Cosecant x = 1 / sin x = hypotenuse / opposite
(Adjacent / hypotenuse) * (hypotenuse / opposite) = Adjacent / opposite = Cotangent x.
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and 
is between 
and 
. What is the value of 
?
For 
to 
, we know that 
. So, the question asks, what is the value of 
, where 
. Therefore, it is asking what the value of 
is, which is 
.
For
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To the nearest 
, what is the cosine formed from the origin to 
? Assume counterclockwise rotation.
To the nearest
If the point to be reached is 
, then we may envision a right triangle with sides 
and 
, and hypotenuse 
. The Pythagorean Theorem tells us that 
, so we plug in and find that: 
Thus, 
Now, SOHCAHTOA tells us that 
, so we know that:
Thus, our cosine is approximately 
.
If the point to be reached is
Thus,
Now, SOHCAHTOA tells us that
Thus, our cosine is approximately
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Two drivers race to a finish line. Driver A drives north 
blocks, and east 
blocks and crosses the goal. Driver B drives the shortest direct route between the two points. Relative to east, what is the cosine of the angle at which Driver B raced? Round to the nearest 
.
Two drivers race to a finish line. Driver A drives north
If the point to be reached is 
blocks north and 
blocks east, then we may envision a right triangle with sides 
and , and hypotenuse . The Pythagorean Theorem tells us that , so we plug in and find that: 
Thus, 
Now, SOHCAHTOA tells us that 
, so we know that:
Thus, our cosine is approximately 
.
If the point to be reached is
Thus,
Now, SOHCAHTOA tells us that
Thus, our cosine is approximately
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