Trigonometry Basics: Sine Values

If sin A = 1/3 in a right triangle ABC, what is the ratio of the lengths of sides BC and AC?

If tan A = 3/4, what is the value of cos A?

If cos A = 2/3, what is the value of sin A?

If AB = 2√2 k, what is the value of cot A?

If AC = 5k, what is the value of sec A?

If sin A = 1/2, what is the value of cos A?

If tan A = 1/2, what is the value of cot A?

If cos A = 3/5, what is the value of sin A?

If AB = 3k, what is the value of tan A?

If AC = 3√2 k, what is the value of csc A?

Trigonometric Ratios

The table shows the values of trigonometric ratios for angles 0° to 90°:
- sin A: 0 to 1
- cos A: 1 to 0
- tan A: 0 to not defined
- cosec A: not defined to 1
- sec A: 1 to not defined
- cot A: not defined to 0

Using Trigonometric Ratios

Example: In a right-angled triangle ABC, with AB = 5 cm and ∠ACB = 30°, find the lengths of BC and AC.
To find the length of BC, use the trigonometric ratio involving BC and the given side AB.

Trigonometric Identities

A trigonometric identity is an equation involving trigonometric ratios of an angle that is true for all values of the angle(s) involved.
Example: In a right-angled triangle ABC, with AB^2 + BC^2 = AC^2, we can derive the identity:
- cos^2 A + sin^2 A = 1
- 1 + tan^2 A = sec^2 A

Finding Trigonometric Ratios

If we know one trigonometric ratio, we can find the others.
Example: If sin A = 1/3, then we can find the lengths of the sides of the triangle and hence the other trigonometric ratios.

Important Points

The value of sin A or cos A is always less than 1 (or equal to 1) in a right triangle.
The hypotenuse is the longest side in a right triangle.

This quiz covers the basics of trigonometry, including sine values for different angles. Test your understanding of trigonometric concepts and formulas.