{"id":5058,"date":"2026-02-01T18:14:46","date_gmt":"2026-02-01T12:44:46","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=5058"},"modified":"2026-02-01T18:15:01","modified_gmt":"2026-02-01T12:45:01","slug":"trigonometric-table-from-0-to-360-cos-sin-cot-tan-sec-cosec","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/trigonometric-table-from-0-to-360-cos-sin-cot-tan-sec-cosec\/","title":{"rendered":"Trigonometric table from 0 to 360 (cos -sin-cot-tan-sec-cosec)"},"content":{"rendered":"\n

Trigonometric ratios are important module in Maths. Here in this post, I will provide Trigonometric table from 0 to 360 (cos -sin-cot-tan-sec-cosec) and also the easy and simple way to remember it.<\/p>\n\n\n\n

Trigonometric table for 0 to 90 is given by<\/u><\/p>\n\n\n\n

\"Trigonometric<\/a><\/figure>\n\n\n\n

And this can be easily remember by below method<\/p>\n\n\n\n

How to easily remember trigonometric ratios table<\/a><\/p>\n\n\n\n

Trigonometric table(sin-cos-tan table) for 0 to 360 is given by<\/span><\/p>\n\n\n\n

\"Trigonometric<\/figure>\n\n\n\n

Now to remember the Trigonometric table for 120 to 360 , we just to need to remember sign of the functions in the four quadrant. We can use below phrase to remember<\/u><\/p>\n\n\n\n

ALL SILVER TEA CUPS<\/strong><\/p>\n\n\n\n

A<\/strong>LL  –  All the trigonometric function are positive in Ist Quadrant<\/p>\n\n\n\n

S<\/strong>ILVER – sin and cosec  function are positive ,rest are negative in II Quadrant<\/p>\n\n\n\n

T <\/strong>EA – tan and cot function are positive, rest are negative in III Quadrant<\/p>\n\n\n\n

C<\/strong>UPS – cos and sec function are positive , rest are negative in IV quadrant<\/p>\n\n\n\n

Now we can use  the formula in below table to calculate the ratios from 120 to 360<\/p>\n\n\n\n

\"sin<\/a><\/figure>\n\n\n\n

This table is very easy to remember, as each correspond to same function.The sign is decided by the corresponding sign of the trigonometric function of the angle in the quadrant<\/p>\n\n\n\n

For example<\/p>\n\n\n\n

a. $ \\cos 120 = \\cos (180 -60) = – \\cos 60$  . It is easy to remember and sign is decided by the angle quadrant. Since 120 lies in II quadrant ,cos is negative<\/p>\n\n\n\n

b.$\\sin 120 = \\cos (180 -60) = \\sin 60$. Here since sin is positive in II quadrant, we put positive sign<\/p>\n\n\n\n

c. $\\tan 120 = \\tan (180 -60) = – \\tan 60$. Here since tan is negative in II quadrant, we put negative sign<\/p>\n\n\n\n

Now Trigonometric table for 120 to 180 is given by<\/strong><\/p>\n\n\n\n

\"Trigonometric<\/a><\/figure>\n\n\n\n

And it is calculated as<\/p>\n\n\n\n

$\\sin (120) = \\sin (180 -60) =\\sin 60= \\frac {\\sqrt {3}}{2}$<\/p>\n\n\n\n

$\\cos (120) = \\cos (180 -60) =- \\cos 60= – \\frac {1}{2}$<\/p>\n\n\n\n

$\\tan 120 = \\frac {\\sin 120}{\\cos 120} = -\\sqrt {3}$<\/p>\n\n\n\n

$\\sin (135) = \\sin (180 -45) = \\sin 45= \\frac {1}{\\sqrt {2}}$<\/p>\n\n\n\n

$\\cos (135) = \\cos (180 -45) =- \\cos 45= -\\frac {1}{\\sqrt {2}}$<\/p>\n\n\n\n

$\\tan 135 = \\frac {\\sin 135}{ \\cos 135} = -1$<\/p>\n\n\n\n

$\\sin (180) = \\sin (180 -0) =sin 0= 0$<\/p>\n\n\n\n

$\\cos (180) = \\cos (180 -0) =-cos 0= -1$<\/p>\n\n\n\n

$\\tan 180 = \\frac {\\sin 180}{\\cos 180} = 0$<\/p>\n\n\n\n

$\\csc 120 = \\frac {1}{\\sin 120} = \\frac {2}{\\sqrt 3}$ <\/p>\n\n\n\n

$\\sec 120 = \\frac {1}{\\cos 120} = -2$<\/p>\n\n\n\n

$\\cot 120 = \\frac {1}{\\tan 120} = – \\frac {1}{\\sqrt 3}$<\/p>\n\n\n\n

$\\csc 135 = \\frac {1}{\\sin 135} = \\sqrt 2$ <\/p>\n\n\n\n

$\\sec 135 = \\frac {1}{\\cos 135} = -\\sqrt 2$<\/p>\n\n\n\n

$\\cot 135 = \\frac {1}{\\tan 135} = – 1$<\/p>\n\n\n\n

Now Trigonometric table for 210 to 270 is given by<\/strong><\/p>\n\n\n\n

\"sin<\/a><\/figure>\n\n\n\n

And it is calculated as<\/p>\n\n\n\n

$\\sin (210) = \\sin (180 +30) =- \\sin 30= -\\frac {1}{2}$<\/p>\n\n\n\n

$\\cos (210) = \\cos (180 +30) =- \\cos 30=-\\frac {\\sqrt {3}}{2}$<\/p>\n\n\n\n

$\\tan (210) = \\frac {\\sin 210}{ \\cos 210} = \\frac {1}{\\sqrt {3}}$<\/p>\n\n\n\n

$\\sin (225) = \\sin (180 +45) =- \\sin 45= -\\frac {1}{\\sqrt {2}}$<\/p>\n\n\n\n

$\\cos (225) = \\cos (180+45) =- \\cos 45= -\\frac {1}{\\sqrt {2}}$<\/p>\n\n\n\n

$\\tan 225 = \\frac {\\sin 225}{\\cos 225} = 1$<\/p>\n\n\n\n

$\\sin (270) = \\sin (180 +90) =- \\sin 90= -1$<\/p>\n\n\n\n

$\\cos (270) = \\cos (180+90) =- \\cos 90= 0$<\/p>\n\n\n\n

$\\tan 270 = \\frac {\\sin 270}{\\cos 270} = -\\frac {1}{0}$ Undefined value<\/p>\n\n\n\n

$\\csc (210) = \\frac {1}{\\sin (210)} = -2$<\/p>\n\n\n\n

$\\sec (210) = \\frac {1}{\\cos (210)}=-\\frac {2}{\\sqrt 3}$<\/p>\n\n\n\n

$\\cot (210) = \\frac {1}{\\tan (210)} = \\sqrt {3}$<\/p>\n\n\n\n

$\\csc (225) = \\frac {1}{\\sin 225}= -\\sqrt {2}$<\/p>\n\n\n\n

$\\sec (225) = \\frac {1}{\\cos 225}= -\\sqrt {2}$<\/p>\n\n\n\n

$\\cot 225 = \\frac {1}{\\tan 225} = 1$<\/p>\n\n\n\n

Now Trigonometric table for 300 to 360 is given by<\/strong><\/p>\n\n\n\n

\"cos<\/a><\/figure>\n\n\n\n

$\\sin (300) = \\sin (360 -60) =- \\sin 60=-\\frac {\\sqrt {3}}{2}$<\/p>\n\n\n\n

$\\cos (300) = \\cos (360-60) =\\cos 60=\\frac {1}{2}$<\/p>\n\n\n\n

$\\tan (300) = \\frac {\\sin 300}{\\cos 300} = -{\\sqrt {3}}$<\/p>\n\n\n\n

$\\sin (315) = \\sin (360 -45) =- \\sin 45= -\\frac {1}{\\sqrt {2}}$<\/p>\n\n\n\n

$\\cos (315) = \\cos (360-45) =\\cos 45= \\frac {1}{\\sqrt {2}}$<\/p>\n\n\n\n

$\\tan 315 = \\frac {\\sin 315}{ \\cos 315} =- 1$<\/p>\n\n\n\n

$\\sin (360) = \\sin (360 -0) =- \\sin 0=0$<\/p>\n\n\n\n

$\\cos (360) = \\cos (360-0) =\\cos 0=1$<\/p>\n\n\n\n

$\\tan (360) = \\frac {\\sin 360}{\\cos 360} = 0$<\/p>\n\n\n\n

$\\csc (300) = \\frac {1}{\\sin (300)}=-\\frac {2}{\\sqrt 3}$<\/p>\n\n\n\n

$\\sec (300) = \\frac {1}{\\cos (300)}=2$<\/p>\n\n\n\n

$\\cot (300) = \\frac {1}{\\tan 300} = -\\frac {1}{\\sqrt {3}}$<\/p>\n\n\n\n

How to calculate the trigonometric ratios of negative of the   angle from 0 to 360<\/strong><\/p>\n\n\n\n

This is quite simple.Just remember this single thing<\/p>\n\n\n\n

$\\cos( x) = \\cos (-x)$  and $\\sec(x) = \\sec(-x)$<\/p>\n\n\n\n

For rest all ratios<\/p>\n\n\n\n

$\\sin (x) = – \\sin(-x)$ , $\\csc (x) = – \\csc (-x)$<\/p>\n\n\n\n

$\\tan (x) = – \\tan (-x)$ , $\\cot (x) = – \\cot(-x)$<\/p>\n\n\n\n

So we can find negative of any angle as<\/p>\n\n\n\n

$\\cos (-120) = \\cos (120) = \\cos (180 -60) =- \\cos 60 = -\\frac {1}{2}$<\/p>\n\n\n\n

$\\sin (-120)= – \\sin(120) = – \\sin 60 = – \\frac {\\sqrt {3}}{2}$<\/p>\n\n\n\n

We have explained everything is terms of degrees, same thing can be done in radian form also<\/p>\n\n\n\n

Related Posts<\/strong><\/p>\n\n\n\nTrigonometric functions<\/a>
Domain ,Range and Graphs of Trigonometric functions<\/a>
Trigonometric equations<\/a>
trigonometry formulas for class 11<\/a>
Sin 15 degrees<\/a><\/a>
 Sin 18 degrees<\/a>
https:\/\/en.wikipedia.org\/wiki\/Trigonometry<\/a>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Trigonometric ratios are important module in Maths. Here in this post, I will provide Trigonometric table from 0 to 360 (cos -sin-cot-tan-sec-cosec) and also the easy and simple way to remember it. Trigonometric table for 0 to 90 is given by And this can be easily remember by below method How to easily remember trigonometric […]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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ratios are important module in Maths. 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Trigonometric table for 0 to 90 is given by And this can be easily remember by below method How to easily remember trigonometric…","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/5058","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/comments?post=5058"}],"version-history":[{"count":3,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/5058\/revisions"}],"predecessor-version":[{"id":9886,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/5058\/revisions\/9886"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=5058"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=5058"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=5058"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}