Trigonometric ratios of specific angles

For five angles, the ratios have exact values. They come from half of a square and half of an equal-sided triangle. You use them as fixed numbers in a sum.

• 30°: sin = 1/2, cos = √3/2, tan = 1/√3.
• 45°: sin = cos = 1/√2, tan = 1.
• 60°: sin = √3/2, cos = 1/2, tan = √3.
• 0°: sin = 0, cos = 1, tan = 0. At 90°: sin = 1, cos = 0, and tan is not defined.

A small example

Find 2 tan 45° + cos 60°. Put in tan 45° = 1 and cos 60° = 1/2. The sum is 2 × 1 + 1/2 = 5/2. Notice that sin 30° and cos 60° are both 1/2. The same pairing holds for sin 60° and cos 30°.

Where marks go

CBSE's 2026-27 Maths sample papers do not allow calculators. So these values have to be recalled. Question 14 of the Maths Basic sample paper asks for sin² 60° − 2 tan² 45° − cos² 30°. With the right values it comes to −2.

It is a multiple-choice question. The 2026-27 Maths Basic marking scheme says Section A questions carry no part marks. There is no step marking here. One wrong value picks a wrong option and scores 0 of the 1 mark. In longer sums, such as an angle of elevation question, a wrong value affects every line after it.

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