Trigonometry » Cosine

The following formula is for the cosine:
cos(A) = adjacent shorter side of Ahypotenuse

Check adjacent side and hypotenuse if you need more information about this.

How do you use the cosine?

Use the following plan/steps/method:

1. Draw a sketch if it is not yet given.
2. Write down the rule: cos(...) = ah.
3. Fill in the data that is given.
4. Calculate the unknown value. If necessary, use  2 = 63.

Example 1: Calculate an angle

Question: Calculate A, round your answer to one decimal. Answer: 2. cos(A) = ah 3. cos(A) = 310 4. A = cos-1(310) ≈ 72.5°

Note to step 4:
- On your calculator, you do: [2nd] or [shift] cos (3 : 10) ≈ 72.542...
- Sometimes arccos has to be used instead of cos^-1.

Example 2: Calculate a side

Question:
Given is triangle ABC with B = 20°, C = 90° and BC = 10 m.
Calculate the length of AB, round your answer to one decimal.

Answer:

1.	Draw a sketch first.

2. cos(B) = ah

3. cos(20°) = 10?

4.	Use 2 = 63
	The ? is at the location of the 3. To get 3, you have to do 6 : 2. Looking back to step 3, we have to do 10 : cos(20°). AB = 10 : cos(20°) ≈ 10.6 m

Note to step 4:

-	You do not have to key in the °-sign on the calculator.
-	Some calculators do not automatically put a '(' behind cos. If you want you can just key in 10 : cos 20.

Example 3: Calculate a side

Question:
Given is triangle PQR with P = 24°, Q = 90° and PR = 42.
Calculate the length of QR, round your answer to one decimal.

Answer:

1.	Draw a sketch first.

2. cos(P) = ah

3. cos(24°) = ?42

4.	Use 2 = 63
	The ? is at the location of the 6. To get 6, you have to do 2 × 3. Looking back to step 3, we have to do cos(24°) × 42. QR = cos(24°) × 42 ≈ 38.4 m

Note to step 4:

-	You do not have to key in the °-sign on the calculator.
-	Some calculators do not automatically put a '(' behind cos. If you want you can just key in cos 24 × 42.