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Values at 0, 30, 45, 60 and 90 degrees

These are the standard trigonometric values of sine, cosine, tangent, cosecant, secant, and cotangent for key angles used in Class 10.

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Student-friendly explanation

The values at 0 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees are memorized because they help solve many direct exam questions quickly. Students should know the pattern of zeros, ones, and root fractions, and also remember where tangent and cotangent become undefined.

How to write this in exams

  1. 1

    Start with the exact idea

    These are the standard trigonometric values of sine, cosine, tangent, cosecant, secant, and cotangent for key angles used in Class 10.

  2. 2

    Then show how to use it

    1. Identify the special angle. 2. Recall the matching standard value. 3. Check whether the function is sine, cosine, tangent, cosecant, secant, or cotangent. 4. Write the exact value carefully.

  3. 3

    Add one concrete example

    sin 30 degrees = 1/2, cos 60 degrees = 1/2, tan 45 degrees = 1.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to swap the values of 30 degrees and 60 degrees. That happens when students memorize only one side of the table.

Definition

These are the standard trigonometric values of sine, cosine, tangent, cosecant, secant, and cotangent for key angles used in Class 10.

Example

sin 30 degrees = 1/2, cos 60 degrees = 1/2, tan 45 degrees = 1.

Rule to remember

Standard values: sin 0 = 0, sin 30 = 1/2, sin 45 = 1/root 2, sin 60 = root 3/2, sin 90 = 1; cos 0 = 1, cos 30 = root 3/2, cos 45 = 1/root 2, cos 60 = 1/2, cos 90 = 0; tan 0 = 0, tan 30 = 1/root 3, tan 45 = 1, tan 60 = root 3, tan 90 is not defined.

Memory hook

Thirty and sixty are mirror angles; forty-five is the equal-side angle.

Examples and method

Worked example

For 60 degrees, sin 60 degrees = root 3 over 2 and cos 60 degrees = 1 over 2. For 45 degrees, tan 45 degrees = 1 because the opposite and adjacent sides are equal.

Method to apply

1. Identify the special angle. 2. Recall the matching standard value. 3. Check whether the function is sine, cosine, tangent, cosecant, secant, or cotangent. 4. Write the exact value carefully.

Diagram support

A simple value table or a triangle-based derivation diagram helps, especially for the 30-60-90 and 45-45-90 triangles.

How CBSE asks it

CBSE often asks for direct values, simplification using standard angles, or checking whether a written table entry is correct.

Avoid common mistakes

Common confusion

Students sometimes interchange 30 degrees and 60 degrees values or forget that tan 90 degrees is not defined.

Common wrong answer

A common wrong answer is to swap the values of 30 degrees and 60 degrees. That happens when students memorize only one side of the table.

Exam tip

Write the table in pairs: sine rises from 0 to 1, while cosine falls from 1 to 0.

Quick check

What is the value of cos 30 degrees and tan 45 degrees?

cos 30 degrees is root 3 over 2, and tan 45 degrees is 1. These are standard values that should be memorized clearly.

Answer writing and exam use

1-mark answer

These are the standard trigonometric values of sine, cosine, tangent, cosecant, secant, and cotangent for key angles used in Class 10.

2-mark answer

These are the standard trigonometric values of sine, cosine, tangent, cosecant, secant, and cotangent for key angles used in Class 10. Standard values: sin 0 = 0, sin 30 = 1/2, sin 45 = 1/root 2, sin 60 = root 3/2, sin 90 = 1; cos 0 = 1, cos 30 = root 3/2, cos 45 = 1/root 2, cos 60 = 1/2, cos 90 = 0; tan 0 = 0, tan 30 = 1/root 3, tan 45 = 1, tan 60 = root 3, tan 90 is not defined. sin 30 degrees = 1/2, cos 60 degrees = 1/2, tan 45 degrees = 1.

3-mark answer

The values at 0 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees are memorized because they help solve many direct exam questions quickly. Students should know the pattern of zeros, ones, and root fractions, and also remember where tangent and cotangent become undefined. Standard values: sin 0 = 0, sin 30 = 1/2, sin 45 = 1/root 2, sin 60 = root 3/2, sin 90 = 1; cos 0 = 1, cos 30 = root 3/2, cos 45 = 1/root 2, cos 60 = 1/2, cos 90 = 0; tan 0 = 0, tan 30 = 1/root 3, tan 45 = 1, tan 60 = root 3, tan 90 is not defined. For 60 degrees, sin 60 degrees = root 3 over 2 and cos 60 degrees = 1 over 2. For 45 degrees, tan 45 degrees = 1 because the opposite and adjacent sides are equal. CBSE often asks for direct values, simplification using standard angles, or checking whether a written table entry is correct. A common wrong answer is to swap the values of 30 degrees and 60 degrees. That happens when students memorize only one side of the table.
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