All ACT Math Resources
Example Questions
Example Question #133 :Trigonometry
The value of a cosine is positive in which quadrants?
The 3rd only
The 1st and 4th
The 1st and 3rd
The 4th only
The 1st and 4th
The cosine is positive in the 1stand 4thquadrants and negative in 2ndand 3rd
Example Question #134 :Trigonometry
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.
Example Question #135 :Trigonometry
andis betweenand. What is the value of?
Forto, we know that. So, the question asks, what is the value of, where. Therefore, it is asking what the value of是,这是.
Example Question #136 :Trigonometry
To the nearest, what is the cosine formed from the origin to? Assume counterclockwise rotation.
If the point to be reached is, then we may envision a right triangle with sidesand, and hypotenuse. The Pythagorean Theorem tells us that, so we plug in and find that:
Thus,
Now,SOHCAHTOAtells us that, so we know that:
Thus, our cosine is approximately.
Example Question #137 :Trigonometry
两个司机比赛终点。司机一个驱动器northblocks, and eastblocks 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.
If the point to be reached isblocks north andblocks east, then we may envision a right triangle with sidesand, and hypotenuse. The Pythagorean Theorem tells us that, so we plug in and find that:
Thus,
Now,SOHCAHTOAtells us that, so we know that:
Thus, our cosine is approximately.