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# Cosine

Trigonometry gets a lot more fun when we start using cosine. But what exactly is cosine? How do we use it? Let''s find out:

## Cosine, explained

The cosine of an angle is expressed in a trigonometric ratio. This ratio states that:

Cosine = the length of the adjacent side divided by the length of the hypotenuse.

You might recall that the hypotenuse is always the side opposite the right angle. The adjacent angle is neither the hypotenuse nor the opposite side, but rather the side next to the angle.

In other words:

cosine = (length of the leg adjacent to the angle) / (length of hypotenuse)

abbreviated as
Cos(θ) = a/h

## Visualizing cosine

As always, it helps to visualize this concept. Let''s take a look:

In this triangle, the cosine of angle A would be

4/5
, while the cosine of angle C would be
3/5
.
Cos(A)=4/5
Cos(C)=3/4

There are a number of interesting things to keep in mind when dealing with cosine:

• The cosine ratio remains the same regardless of the size of the triangle
• We can consider the cosine ratio to be a function
• The reciprocal of the cosine ratio is the "secant" ratio -- abbreviated as "sec"
• secant= length of the hypotenuse /length of the leg adjacent to the angle

## Topics related to the Cosine

Amplitude and Period of Sine and Cosine Functions

Cosine Function

Law of Cosines

## Flashcards covering the Cosine

Trigonometry Flashcards

CLEP Precalculus Flashcards

## Practice tests covering the Cosine

Trigonometry Diagnostic Tests

Precalculus Diagnostic Tests

## Pair your student with a tutor who can explain cosine

Cosine, tangent, and sine are concepts that your student needs to get right the first time around, and a tutor can help them establish confidence in these topics with extra help after class. They can use examples that match your student''s hobbies -- perhaps using sports to explain triangles, for instance. Your student can also receive targeted instruction based on their learning style. Varsity Tutors will match your student with a suitable tutor, so reach out today to get started.

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