Sin 45 Cos 30 Cos 45 Sin 30

What is value of sin 30?

What about cos 0?

and sin 0?

How exercise we recollect them?

Let’s learn how. We volition talk over what are unlike values of


sin, cos, tan, cosec, sec, cot


at


0, xxx, 45, 60 and 90 degrees


and how to memorise them.

And so, we have to fill this tabular array

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How to notice the values?

To learn the table, we should offset know how sin cos tan are related

Nosotros know that

• tan θ = sin θ/cosθ
• sec θ = 1/cos θ
• cosec θ = 1/sin θ
• cot θ = 1/cot θ

Now let u.s.a. discuss unlike values

For sin

For memorising sin 0°, sin thirty°, sin 45°, sin lx° and sin ninety°

We should larn information engineering similar

1. sin 0° =
   
   
   0
   
2. sin thirty° =
   
   
   i/2
   
3. sin 45° =
   
   
   1/√2
   
4. sin sixty° =
   
   
   √iii/two
   
5. sin xc° =
   
   
   ane
   

And so, our pattern will be similar

0, 1/2,  one/√ii,  √3/two,  1

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For cos

For memorising cos 0°, cos 30°, cos 45°, cos lx° and cos ninety°

Cos is the opposite of sin.

Nosotros should acquire information technology similar

1. cos 0° = sin xc° =
   
   
   1
   
2. cos 30° = sin sixty° = √iii/ii
3. cos 45° = sin 45° =
   
   
   i/√2
   
4. cos 60° = sin 30° =
   
   
   one/2
   
5. cos 90° = sin 0° =
   
   
   0
   

So, for cos, it volition exist like

one, √three/two,  ane/√2,  one/2,  0

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For tan

We know that tan θ = sin θ /cos θ

So, it will be

• tan 0° = sin 0° / cos 0° = 0/1 =
  
  
  0
  
• tan 30° = sin thirty° / cos xxx° = (one/2)/ (√3/2) =
  
  
  1/√3
  
• tan 45° = sin 45° / cos 45° = (i/√2)/ (ane/√ii) =
  
  
  one
  
• tan threescore° = sin sixty° / cos 60° = (√three/2) / (i/ii) =
  
  
  √3
  
• tan xc° = sin 90° / cos ninety° = ane/0 = Non Divers =
  
  
  ∞
  

So, for tan, it is

0, 1/√3, 1, √three, ∞

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For cosec

Nosotros know that

cosec θ = 1/sin θ

For sin, we know

0, ane/2,  i/√2,  √iii/ii,  i

So, for cosec it volition be

• cosec 0° = 1 / sin 0° = one/0 = Not Defined =
  
  
  ∞
  
• cosec xxx° = 1 / sin xl° = 1/(one/2) =
  
  
  ii
  
• cosec 45° = i / sin 45° = 1/(ane/√ii) =
  
  
  √2
  
• cosec lx° = 1 / sin lx° = 1/(√three/2) =
  
  
  2/√iii
  
• cosec xc° = i / sin 90° = i/ane =
  
  
  i
  

And then, for cosec, it is

∞, 2, √two, 2/√3, 1

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For sec

We know that

sec θ = 1/cos θ

For cos, we know

1, √3/2,  i/√2,  i/2,  0

So, for sec information technology will exist

• sec 0° = one / cos 0° = 1/i =
  
  
  1
  
• sec 30° = ane / cos 40° = one/(√3/2) =
  
  
  2/√3
  
• sec 45° = 1 / cos 45° = i/(ane/√ii) =
  
  
  √2
  
• sec threescore° = i / cos 60° = 1/(i/2) =
  
  
  2
  
• sec xc° = one / cos 90° = one/0 = Non Defined =
  
  
  ∞
  

So, for sec, it is

1, 2/√3, √two,


ii,


∞

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For cot

Nosotros know that

cot θ = ane/tan θ

For tan, we know that

0, one/√three, 1, √3, ∞

Then, for cot information technology will be

• cot 0° = i / tan 0° = one/0 = Non Divers =
  
  
  ∞
  
• cot xxx° = 1 / tan xxx° = i/(1/√three) =
  
  
  √iii
  
• cot 45° = one / tan 45° = i/i =
  
  
  1
  
• cot lx° = ane / tan 60° = ane/√3
• cot xc° = i / tan 90° = 1/∞ =
  
  
  0
  

So, for cot, information technology is

∞, √3, 1, 1/√3, 0

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And and so, our full tabular array looks similar this

Y’all can also practise questions past clicking


Side by side.

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Trigonometry Table

Trigonometry Table has all the values of sin, cos, tan for all angles from 0 to 90 degree.

Y’all can likewise download it below

Radian	Caste	Sine	Cosine	Tangent	Radian	Caste	Sine	Cosine	Tangent
0.000	0	0.000	i.000	0.000	0.803	46	0.719	0.695	1.036
0.017	1	0.017	1.000	0.017	0.820	47	0.731	0.682	i.072
0.035	two	0.035	0.999	0.035	0.838	48	0.743	0.669	1.111
0.052	3	0.052	0.999	0.052	0.855	49	0.755	0.656	ane.150
0.070	4	0.070	0.998	0.070	0.873	l	0.766	0.643	1.192
0.087	5	0.087	0.996	0.087	0.890	51	0.777	0.629	one.235
0.105	six	0.105	0.995	0.105	0.908	52	0.788	0.616	1.280
0.122	seven	0.122	0.993	0.123	0.925	53	0.799	0.602	i.327
0.140	8	0.139	0.990	0.141	0.942	54	0.809	0.588	ane.376
0.157	ix	0.156	0.988	0.158	0.960	55	0.819	0.574	1.428
0.175	10	0.174	0.985	0.176	0.977	56	0.829	0.559	one.483
0.192	11	0.191	0.982	0.194	0.995	57	0.839	0.545	1.540
0.209	12	0.208	0.978	0.213	1.012	58	0.848	0.530	one.600
0.227	13	0.225	0.974	0.231	i.030	59	0.857	0.515	ane.664
0.244	xiv	0.242	0.970	0.249	1.047	sixty	0.866	0.500	i.732
0.262	xv	0.259	0.966	0.268	one.065	61	0.875	0.485	1.804
0.279	sixteen	0.276	0.961	0.287	one.082	62	0.883	0.469	1.881
0.297	17	0.292	0.956	0.306	1.100	63	0.891	0.454	one.963
0.314	18	0.309	0.951	0.325	i.117	64	0.899	0.438	2.050
0.332	xix	0.326	0.946	0.344	one.134	65	0.906	0.423	ii.145
0.349	xx	0.342	0.940	0.364	1.152	66	0.914	0.407	two.246
0.367	21	0.358	0.934	0.384	1.169	67	0.921	0.391	ii.356
0.384	22	0.375	0.927	0.404	ane.187	68	0.927	0.375	2.475
0.401	23	0.391	0.921	0.424	1.204	69	0.934	0.358	ii.605
0.419	24	0.407	0.914	0.445	1.222	lxx	0.940	0.342	ii.747
0.436	25	0.423	0.906	0.466	ane.239	71	0.946	0.326	2.904
0.454	26	0.438	0.899	0.488	ane.257	72	0.951	0.309	3.078
0.471	27	0.454	0.891	0.510	ane.274	73	0.956	0.292	3.271
0.489	28	0.469	0.883	0.532	1.292	74	0.961	0.276	three.487
0.506	29	0.485	0.875	0.554	1.309	75	0.966	0.259	three.732
0.524	30	0.500	0.866	0.577	1.326	76	0.970	0.242	4.011
0.541	31	0.515	0.857	0.601	one.344	77	0.974	0.225	four.331
0.559	32	0.530	0.848	0.625	1.361	78	0.978	0.208	iv.705
0.576	33	0.545	0.839	0.649	1.379	79	0.982	0.191	5.145
0.593	34	0.559	0.829	0.675	ane.396	80	0.985	0.174	5.671
0.611	35	0.574	0.819	0.700	1.414	81	0.988	0.156	half-dozen.314
0.628	36	0.588	0.809	0.727	i.431	82	0.990	0.139	seven.115
0.646	37	0.602	0.799	0.754	1.449	83	0.993	0.122	eight.144
0.663	38	0.616	0.788	0.781	1.466	84	0.995	0.105	9.514
0.681	39	0.629	0.777	0.810	ane.484	85	0.996	0.087	eleven.430
0.698	forty	0.643	0.766	0.839	1.501	86	0.998	0.070	14.301
0.716	41	0.656	0.755	0.869	1.518	87	0.999	0.052	xix.081
0.733	42	0.669	0.743	0.900	ane.536	88	0.999	0.035	28.636
0.750	43	0.682	0.731	0.933	1.553	89	one.000	0.017	57.290
0.768	44	0.695	0.719	0.966	1.571	xc	i.000	0.000	∞
0.785	45	0.707	0.707	ane.000

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