Question

trignometery ratios of complementery angles''''.... ✨✨✨✨​

Answer 1

SOLUTION:

✯ Trigonometric ratios of complementary angles ✯

➾ $\sf{ sin( 90^° - \theta) = cos \theta}$

➾ $\sf{ cos( 90^° - \theta) = sin \theta }$

➾ $\sf{ tan( 90^° - \theta) = cot \theta }$

➾ $\sf{ cot( 90^° - \theta) = tan \theta}$

➾ $\sf{ sec( 90^° - \theta) = cosec \theta }$

➾ $\sf{ cosec( 90^° - \theta) = sec \theta }$

________________

✯ Trigonometric ratios of 0° ✯

➨ $\sf{ sin 0^°= 0}$

➨ $\sf{ cos 0^° = 1}$

➨ $\sf{ tan 0^° = 0}$

➨ $\sf{ cot 0^° = not\:defined}$

➨ $\sf{ sec 0^° = 1}$

➨ $\sf{ cosec 0^° = not\: defined}$

________________

✯ Trigonometric ratios of 30° ✯

➛ $\sf{ sin 30^° = \frac{1}{2}}$

➛ $\sf{ cos 30^° = \frac{\sqrt{3}}{2}}$

➛ $\sf{ tan 30^° = \frac{1}{\sqrt{3}}}$

➛ $\sf{ cot 30^° = \sqrt{3}}$

➛ $\sf{ sec 30^° = \frac{2}{\sqrt{3}}}$

➛ $\sf{ cosec 30^° = 2}$

_________________

✯ Trigonometric ratios of 45° ✯

➧ $\sf{ sin 45^° = \frac{1}{\sqrt{2}}}$

➧ $\sf{ cos 45^° = \frac{1}{\sqrt{2}}}$

➧ $\sf{ tan 45^° = 1}$

➧ $\sf{ cot 45^° = 1 }$

➧ $\sf{ sec 45^° = \sqrt{2}}$

➧ $\sf{ cosec 45^° = \sqrt{2}}$

________________

✯ Trigonometric ratios of 60° ✯

➫ $\sf{ sin 60^° = \frac{\sqrt{3}}{2}}$

➫ $\sf{ cos 60^° = \frac{1}{2}}$

➫ $\sf{ tan 60^° = \sqrt{3}}$

➫ $\sf{ cot 60^° = \frac{1}{\sqrt{3}}}$

➫ $\sf{ sec 60^° = 2}$

➫ $\sf{ cosec 60^° = \frac{2}{\sqrt{3}}}$

________________

✯ Trigonometric ratios of 90° ✯

➬ $\sf{ sin 90^° = 1}$

➬ $\sf{ cos 90^° = 0}$

➬ $\sf{ tan 90^° = not\:defined}$

➬ $\sf{ cot 90^° = 0}$

➬ $\sf{ sec 90^° = not\: defined}$

➬ $\sf{ cosec 90^° = 1}$

________________

✯ Trigonometric Identities ✯

➸ $\bf\red{ sin^2 \theta + cos^2 \theta = 1}$

➸ $\bf\red{ 1 + tan^2 \theta = sec^2 \theta}$

➸ $\bf\red{ 1 + cot^2 \theta = cosec^2 \theta}$

________________

________________

Answer 2

Answer:

In Mathematics, the complementary angles are the set of two angles such that their sum is equal to 90°. For example, 30° and 60° are complementary to each other as their sum is equal to 90°.

Sin 60∘ = Sin (90∘- 30∘) = Cos 30∘ = 3–√2

Sin 60∘ = Sin (90∘- 30∘) = Cos 30∘ = 3–√2Cos 60∘ = Cos (90∘- 30∘) = Sin 30∘ = 12

Sin 60∘ = Sin (90∘- 30∘) = Cos 30∘ = 3–√2Cos 60∘ = Cos (90∘- 30∘) = Sin 30∘ = 12Tan 60∘ = Tan (90∘- 30∘) = Cot 30∘ = 3–√1

Sin 60∘ = Sin (90∘- 30∘) = Cos 30∘ = 3–√2Cos 60∘ = Cos (90∘- 30∘) = Sin 30∘ = 12Tan 60∘ = Tan (90∘- 30∘) = Cot 30∘ = 3–√1Cosec 60∘ = Cosec (90∘- 30∘) = Sec 30∘ = 23–√

Sin 60∘ = Sin (90∘- 30∘) = Cos 30∘ = 3–√2Cos 60∘ = Cos (90∘- 30∘) = Sin 30∘ = 12Tan 60∘ = Tan (90∘- 30∘) = Cot 30∘ = 3–√1Cosec 60∘ = Cosec (90∘- 30∘) = Sec 30∘ = 23–√Sec 60∘ = Sec (90∘- 30∘) = Cosec 30∘ = 21

Sin 60∘ = Sin (90∘- 30∘) = Cos 30∘ = 3–√2Cos 60∘ = Cos (90∘- 30∘) = Sin 30∘ = 12Tan 60∘ = Tan (90∘- 30∘) = Cot 30∘ = 3–√1Cosec 60∘ = Cosec (90∘- 30∘) = Sec 30∘ = 23–√Sec 60∘ = Sec (90∘- 30∘) = Cosec 30∘ = 21Cot 60∘ = Cot (90∘- 30∘) = Tan 30∘ = 13–