{"id":7593,"date":"2022-09-10T07:28:37","date_gmt":"2022-09-10T07:28:37","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7593"},"modified":"2022-09-10T07:28:37","modified_gmt":"2022-09-10T07:28:37","slug":"inverse-trigonometry-examples","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/10\/inverse-trigonometry-examples\/","title":{"rendered":"Inverse trigonometry Examples"},"content":{"rendered":"\n

If we know the size of an angle, we can find the sin, cos and tan of the angle by using a scientific calculator. We can also use a calculator to find the inverse<\/strong> or reverse of this. If we know the sin, cos or tan of an angle, we can find the size of the angle.<\/p>\n\n\n\n

If tan \u03b8<\/em> = x<\/em> then tan -1<\/sup> x<\/em> = \u03b8<\/em><\/p>\n\n\n\n

If sin \u03b8<\/em> = x<\/em> then sin -1<\/sup> x<\/em> = \u03b8<\/em><\/p>\n\n\n\n

If cos \u03b8<\/em> = x<\/em> then cos -1<\/sup> x<\/em> = \u03b8<\/em><\/p>\n\n\n\n

Example:<\/em><\/strong><\/p>\n\n\n\n

Find the values of \u03b8<\/em> for the following (Give your answers in degrees and minutes):<\/p>\n\n\n\n

a) tan \u03b8<\/em> = 2.53<\/p>\n\n\n\n

b) sin \u03b8<\/em> = 0.456<\/p>\n\n\n\n

c) cos \u03b8<\/em> =<\/em> 0.6647<\/p>\n\n\n\n

Solution:<\/em><\/strong><\/p>\n\n\n\n

a) Press<\/p>\n\n\n\n

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

tan -1<\/sup> 2.53 = 68\u02da 25 \u2019 59.69 \u201d ( The \u201d symbol denotes seconds. There are 60 seconds in 1 minute.)<\/p>\n\n\n\n

= 68\u02da 26 \u2019 (to the nearest minute)<\/p>\n\n\n\n

b) Press<\/p>\n\n\n\n

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

sin -1<\/sup> 0.456 = 27\u02da 7 \u2019 45.46 \u201d<\/p>\n\n\n\n

= 27\u02da 8 \u2019 (to the nearest minute)<\/p>\n\n\n\n

b) Press<\/p>\n\n\n\n

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

cos -1<\/sup> 0.6647 = 48\u02da 20 \u2019 26.47 \u201d<\/p>\n\n\n\n

= 48\u02da 20 \u2019 (to the nearest minute)<\/p>\n\n\n\n

Example:<\/em><\/strong><\/p>\n\n\n\n

Calculate the angle x<\/em> in the figure below. Give your answer correct to 4 decimal places.<\/p>\n\n\n\n

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

Solution:<\/em><\/strong><\/p>\n\n\n\n

sin x<\/em> = <\/p>\n\n\n\n

x<\/em> = sin -1<\/sup>(2.3 \u00f7 8.15)<\/p>\n\n\n\n

= 16.3921\u02da<\/p>\n","protected":false},"excerpt":{"rendered":"

If we know the size of an angle, we can find the sin, cos and tan of the angle by using a scientific calculator. We can also use a calculator to find the inverse or reverse of this. If we know the sin, cos or tan of an angle, we can find the size of the angle. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[482],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7593"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=7593"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7593\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7593"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7593"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7593"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}