medium difficulty6 min

Error detection in standard values

Error detection in standard values means finding and correcting wrong entries in the standard trigonometric value table.

In one line: Thirty and sixty swap, forty-five stays the same, and ninety needs special care.

Practice This Concept

Understand it

This skill is important because CBSE often tests whether students truly know the values or only memorized them partly. The most common errors are swapping 30 degrees and 60 degrees, confusing sine with cosine, and forgetting that tan 90 degrees is not defined. Careful comparison is the best way to catch mistakes.

Example

If a table shows cos 60 degrees as root 3 over 2, that is wrong because cos 60 degrees should be 1/2.

Formula and rule

Standard values must follow the correct table: sin 30 = 1/2, sin 60 = root 3/2, cos 30 = root 3/2, cos 60 = 1/2, tan 45 = 1, and 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

1If a learner writes cos 30 degrees = 1/2, the correction is root 3 over 2.
2This shows the common swap between 30 degrees and 60 degrees.

Method you can reuse

1Locate the angle.
2Recall the correct value from the standard table.
3Compare with the given entry.
4Correct the swapped or mismatched value.

Visual tip

A standard value chart or a 30-60-90 triangle sketch helps detect swapped entries quickly.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A table says sin 60 degrees = 1/2. Is this correct?

Think first, then show answer

No, it is not correct. sin 60 degrees is root 3 over 2, not 1/2. The value 1/2 belongs to sin 30 degrees and cos 60 degrees.

Common wrong answer

A common wrong answer is to trust the written table because it looks neat. In trig, neat does not mean correct.

Don't mix this up

Students often accept a wrong table entry because it looks similar to a correct one.

Exam tip

Check the pair pattern: 30 degrees and 60 degrees are complements, while 45 degrees stays equal in sine and cosine.

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 may present a table with one wrong value and ask students to identify the error, or may ask for the correct value directly.

1
Enough for 1 mark
Error detection in standard values means finding and correcting wrong entries in the standard trigonometric value table.
2
Add for 2 marks
Example: If a table shows cos 60 degrees as root 3 over 2, that is wrong because cos 60 degrees should be 1/2.
3
Add for 3 marks
The most common errors are swapping 30 degrees and 60 degrees, confusing sine with cosine, and forgetting that tan 90 degrees is not defined.

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