Trigonometry » Sine

The following formula is for the sine:
sin(A) = opposite shorter side of Ahypotenuse

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

How do you use the sine?

Use the following plan/steps/method:

1. Draw a sketch if it is not yet given.
2. Write down the rule: sin(...) = oh.
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. sin(A) = oh 3. sin(A) = 4.27.0 4. A = sin-1(4.27.0) ≈ 36.9°

Note to step 4:
- On your calculator, you do: [2nd] or [shift] sin (4.2 : 7.0) ≈ 36.869...
- Sometimes arcsin has to be used instead of sin^-1.

Example 2: Calculate a side

Question:
Given is triangle PQR with P = 22°, Q = 90° and PR = 4.
Calculate the length of QR, round your answer to one decimal.

Answer:

1.	Draw a sketch first.

2. sin(P) = oh

3. sin(22°) = ?4

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 sin(22°) × 4. QR = sin(22°) × 4 ≈ 1.5 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 sin. If you want you can just key in sin 22 × 4.

Example 3: Calculate a side

Question:
Given is triangle ABC with A = 68°, C = 90° and BC = 8.5 m.
Calculate the length of AB, round your answer to one decimal.

Answer:

1.	Draw a sketch first.

2. sin(A) = oh

3. sin(68°) = 8.5?

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 8.5 : sin(68°). AB = 8.5 : sin(68°) ≈ 9.2 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 sin. If you want you can just key in 8.5 : sin 68.