medium difficulty6 min

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.

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

Practice This Concept

Understand it

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.

Example

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

Formula and rule

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.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

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

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

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.

Don't mix this up

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

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

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

1
Enough for 1 mark
These are the standard trigonometric values of sine, cosine, tangent, cosecant, secant, and cotangent for key angles used in Class 10.
2
Add for 2 marks
Example: sin 30 degrees = 1/2, cos 60 degrees = 1/2, tan 45 degrees = 1.
3
Add for 3 marks
For 60 degrees, sin 60 degrees = root 3 over 2 and cos 60 degrees = 1 over 2.

MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results