sin A is one symbol

The idea

sin A is one symbol for the sine of angle A, not a product of 'sin' and A; sin² A means (sin A)², and cosec A = (sin A)⁻¹, which is different from sin⁻¹ A.

What does it say?

You will see sin A, cos A and tan A many times in this chapter.

They look like a word followed by a letter. But what is the word "sin" doing next to the angle A?

What do you think sin A means?

• sin multiplied by A
• One number made from the angle A
• A side of the triangle

Read four symbols

Tap a symbol and choose what it means. The triangle has BC = 3, AB = 4 and AC = 5.

One symbol, one meaning

sin A is one symbol for "the sine of the angle A". It is not the product of "sin" and A. sin² A means (sin A)². cosec A = (sin A)⁻¹, which is different from sin⁻¹ A.

"sin" on its own has no meaning. The same is true for cos, tan, cosec, sec and cot. Sometimes the Greek letter θ (theta) is used for an angle. sin⁻¹ A is read "sine inverse A" and is met in higher classes.

Notes

sin A is one symbol, not sin × A. sin² A means (sin A)². cosec A = (sin A)⁻¹, which is different from sin⁻¹ A.

Check yourself

sin A = 0.6. What is sin² A?

Answer: 0.36

sin² A = (sin A)² = 0.6 × 0.6 = 0.36.

Which is the same as (tan A)²?

sin A = 0.25. What is (sin A)⁻¹, which is cosec A?

Answer: 4

(sin A)⁻¹ = 1 ÷ sin A = 1 ÷ 0.25 = 4. This is cosec A.

Which statement is correct?

• tan² A — correct. Yes! sin² A, cos² A, tan² A and so on are written in place of (sin A)², (cos A)², (tan A)².
• 2 tan A. 2 tan A means two times tan A. A little 2 above the name means "squared".
• tan A². tan A² would mean the tangent of A². The square of the ratio is written tan² A.
• cos A means cos × A.. "cos" alone has no meaning, so cos A cannot be a product.
• cosec A = sin⁻¹ A.. cosec A = (sin A)⁻¹. And sin⁻¹ A (sine inverse A) is a different thing.
• cos A is one symbol; "cos" alone has no meaning. — correct. Yes! cos A is short for "the cosine of the angle A".