Trigonometry & Heights / Distances • Topic 2 of 4

Standard Angle Values

Lock in the table for 0, 30, 45, 60 and 90 degrees. sin runs 0, 1/2, 1/root2, root3/2, 1; cos is the reverse; tan = sin/cos. Most SSC direct questions are just substitutions from this table, so recalling it instantly is worth several marks per paper.

✅ Solved examples

1. Value of sin 60 x cos 30?
(root3/2)(root3/2) = 3/4.
2. tan 45 + cot 45?
1 + 1 = 2.
3. sin^2 30 + cos^2 30?
(1/4) + (3/4) = 1.
4. Value of 2 sin 30 cos 30?
2 x (1/2)(root3/2) = root3/2 (which is sin 60).

✏️ Practice — try these, take hints as needed

1. cos 45 x sin 45?
(1/root2)^2.
1/2.
—
1/2
2. tan 60 x tan 30?
root3 x 1/root3.
—
—
1
3. sin 90 - cos 90?
1 - 0.
—
—
1
4. sec^2 45 - tan^2 45?
Identity = 1.
2 - 1.
—
1
5. 4 sin 30 cos 60?
4 x 1/2 x 1/2.
—
—
1

📝 Topic test — 8 questions

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