ACT Math : How to find positive cosine

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store varsity tutors amazon store varsity tutors ibooks store

Example Questions

Example Question #133 :Trigonometry

The value of a cosine is positive in which quadrants?

Possible Answers:

The 3rd only

The 1st and 4th

The 1st and 3rd

The 4th only

Correct answer:

The 1st and 4th

Explanation:

The cosine is positive in the 1stand 4thquadrants and negative in 2ndand 3rd

Example Question #134 :Trigonometry

Which of the following is equal to?

Possible Answers:

Correct answer:

Explanation:

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?

Possible Answers:

Correct answer:

Explanation:

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.

Possible Answers:

Correct answer:

Explanation:

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.

Possible Answers:

Correct answer:

Explanation:

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.

Learning Tools by Varsity Tutors